:: YONEDA_1 semantic presentation

K145() is Element of K32(K141())
K141() is set
K32(K141()) is set
{} is empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional set
1 is non empty set
{{},1} is non empty set
K140() is set
K32(K140()) is set
K32(K145()) is set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Hom A is non empty set
Ens (Hom A) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
(A) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Hom A is non empty set
Ens (Hom A) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (A) is non empty set
F is Relation-like Function-like set
c is Relation-like Function-like set
F * c is Relation-like Function-like set
c9 is Element of the carrier' of (A)
cod c9 is Element of the carrier of (A)
the carrier of (A) is non empty set
the Target of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
K33( the carrier' of (A), the carrier of (A)) is Relation-like set
K32(K33( the carrier' of (A), the carrier of (A))) is set
the Target of (A) . c9 is Element of the carrier of (A)
g is Element of the carrier' of (A)
dom g is Element of the carrier of (A)
the Source of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
the Source of (A) . g is Element of the carrier of (A)
dom c9 is Element of the carrier of (A)
the Source of (A) . c9 is Element of the carrier of (A)
[(dom c9),(cod c9)] is V1() Element of the carrier of K210((A),(A))
K210((A),(A)) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of K210((A),(A)) is non empty set
{(dom c9),(cod c9)} is non empty set
{(dom c9)} is non empty set
{{(dom c9),(cod c9)},{(dom c9)}} is non empty set
[[(dom c9),(cod c9)],F] is V1() set
{[(dom c9),(cod c9)],F} is non empty set
{[(dom c9),(cod c9)]} is non empty Relation-like Function-like set
{{[(dom c9),(cod c9)],F},{[(dom c9),(cod c9)]}} is non empty set
cod g is Element of the carrier of (A)
the Target of (A) . g is Element of the carrier of (A)
[(dom g),(cod g)] is V1() Element of the carrier of K210((A),(A))
{(dom g),(cod g)} is non empty set
{(dom g)} is non empty set
{{(dom g),(cod g)},{(dom g)}} is non empty set
[[(dom g),(cod g)],c] is V1() set
{[(dom g),(cod g)],c} is non empty set
{[(dom g),(cod g)]} is non empty Relation-like Function-like set
{{[(dom g),(cod g)],c},{[(dom g),(cod g)]}} is non empty set
[(dom c9),(cod g)] is V1() Element of the carrier of K210((A),(A))
{(dom c9),(cod g)} is non empty set
{{(dom c9),(cod g)},{(dom c9)}} is non empty set
[[(dom c9),(cod g)],(F * c)] is V1() set
{[(dom c9),(cod g)],(F * c)} is non empty set
{[(dom c9),(cod g)]} is non empty Relation-like Function-like set
{{[(dom c9),(cod g)],(F * c)},{[(dom c9),(cod g)]}} is non empty set
g (*) c9 is Element of the carrier' of (A)
Maps (Hom A) is non empty set
fDom (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
K33((Maps (Hom A)),(Hom A)) is Relation-like set
K32(K33((Maps (Hom A)),(Hom A))) is set
fCod (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
fComp (Hom A) is Relation-like K33((Maps (Hom A)),(Maps (Hom A))) -defined Maps (Hom A) -valued Function-like Element of K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))))
K33((Maps (Hom A)),(Maps (Hom A))) is Relation-like set
K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))) is Relation-like set
K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A)))) is set
CatStr(# (Hom A),(Maps (Hom A)),(fDom (Hom A)),(fCod (Hom A)),(fComp (Hom A)) #) is strict CatStr
F1 is Element of Maps (Hom A)
cod F1 is Element of Hom A
c9 `1 is set
(c9 `1) `2 is set
[(dom c9),(cod c9)] `2 is set
[(dom g),(cod g)] `1 is set
g `1 is set
(g `1) `1 is set
F2 is Element of Maps (Hom A)
dom F2 is Element of Hom A
dom F1 is Element of Hom A
[(dom F1),(cod F1)] is V1() set
{(dom F1),(cod F1)} is non empty set
{(dom F1)} is non empty set
{{(dom F1),(cod F1)},{(dom F1)}} is non empty set
F1 `2 is Relation-like Function-like set
[[(dom F1),(cod F1)],(F1 `2)] is V1() set
{[(dom F1),(cod F1)],(F1 `2)} is non empty set
{[(dom F1),(cod F1)]} is non empty Relation-like Function-like set
{{[(dom F1),(cod F1)],(F1 `2)},{[(dom F1),(cod F1)]}} is non empty set
cod F2 is Element of Hom A
[(dom F2),(cod F2)] is V1() set
{(dom F2),(cod F2)} is non empty set
{(dom F2)} is non empty set
{{(dom F2),(cod F2)},{(dom F2)}} is non empty set
F2 `2 is Relation-like Function-like set
[[(dom F2),(cod F2)],(F2 `2)] is V1() set
{[(dom F2),(cod F2)],(F2 `2)} is non empty set
{[(dom F2),(cod F2)]} is non empty Relation-like Function-like set
{{[(dom F2),(cod F2)],(F2 `2)},{[(dom F2),(cod F2)]}} is non empty set
[(dom g),(cod g)] `2 is set
(g `1) `2 is set
(c9 `1) `1 is set
[(dom c9),(cod c9)] `1 is set
[g,c9] is V1() Element of the carrier' of K210((A),(A))
the carrier' of K210((A),(A)) is non empty set
{g,c9} is non empty set
{g} is non empty set
{{g,c9},{g}} is non empty set
the Comp of (A) is Relation-like K33( the carrier' of (A), the carrier' of (A)) -defined the carrier' of (A) -valued Function-like Element of K32(K33(K33( the carrier' of (A), the carrier' of (A)), the carrier' of (A)))
K33( the carrier' of (A), the carrier' of (A)) is Relation-like set
K33(K33( the carrier' of (A), the carrier' of (A)), the carrier' of (A)) is Relation-like set
K32(K33(K33( the carrier' of (A), the carrier' of (A)), the carrier' of (A))) is set
proj1 the Comp of (A) is Relation-like set
(fComp (Hom A)) . (F2,F1) is set
[F2,F1] is V1() set
{F2,F1} is non empty set
{F2} is non empty set
{{F2,F1},{F2}} is non empty set
(fComp (Hom A)) . [F2,F1] is set
F2 * F1 is Element of Maps (Hom A)
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
F is Element of the carrier of A
hom?- F is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
the carrier' of A is non empty set
Hom A is non empty set
Maps (Hom A) is non empty set
K33( the carrier' of A,(Maps (Hom A))) is Relation-like set
K32(K33( the carrier' of A,(Maps (Hom A)))) is set
(A) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Ens (Hom A) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (A) is non empty set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
(A) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Hom A is non empty set
Ens (Hom A) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
F is Element of the carrier' of A
cod F is Element of the carrier of A
the carrier of A is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Target of A . F is Element of the carrier of A
(A,(cod F)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
the carrier' of (A) is non empty set
hom?- (cod F) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
Maps (Hom A) is non empty set
K33( the carrier' of A,(Maps (Hom A))) is Relation-like set
K32(K33( the carrier' of A,(Maps (Hom A)))) is set
dom F is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Source of A . F is Element of the carrier of A
(A,(dom F)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom F) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
F1 is Element of the carrier of A
Hom ((cod F),F1) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = F1 ) } is set
Hom ((dom F),F1) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = F1 ) } is set
[(Hom ((cod F),F1)),(Hom ((dom F),F1))] is V1() set
{(Hom ((cod F),F1)),(Hom ((dom F),F1))} is non empty set
{(Hom ((cod F),F1))} is non empty set
{{(Hom ((cod F),F1)),(Hom ((dom F),F1))},{(Hom ((cod F),F1))}} is non empty set
hom (F,F1) is Relation-like Hom ((cod F),F1) -defined Hom ((dom F),F1) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),F1)),(Hom ((dom F),F1))))
K33((Hom ((cod F),F1)),(Hom ((dom F),F1))) is Relation-like set
K32(K33((Hom ((cod F),F1)),(Hom ((dom F),F1)))) is set
[[(Hom ((cod F),F1)),(Hom ((dom F),F1))],(hom (F,F1))] is V1() set
{[(Hom ((cod F),F1)),(Hom ((dom F),F1))],(hom (F,F1))} is non empty set
{[(Hom ((cod F),F1)),(Hom ((dom F),F1))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),F1)),(Hom ((dom F),F1))],(hom (F,F1))},{[(Hom ((cod F),F1)),(Hom ((dom F),F1))]}} is non empty set
(A,(cod F)) . F1 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . F1 is Element of the carrier of (A)
(A,(dom F)) . F1 is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . F1 is Element of the carrier of (A)
Hom (((A,(cod F)) . F1),((A,(dom F)) . F1)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b₁ where b₁ is Element of the carrier' of (A) : ( dom b₁ = (A,(cod F)) . F1 & cod b₁ = (A,(dom F)) . F1 ) } is set
fDom (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
K33((Maps (Hom A)),(Hom A)) is Relation-like set
K32(K33((Maps (Hom A)),(Hom A))) is set
fCod (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
fComp (Hom A) is Relation-like K33((Maps (Hom A)),(Maps (Hom A))) -defined Maps (Hom A) -valued Function-like Element of K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))))
K33((Maps (Hom A)),(Maps (Hom A))) is Relation-like set
K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))) is Relation-like set
K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A)))) is set
CatStr(# (Hom A),(Maps (Hom A)),(fDom (Hom A)),(fCod (Hom A)),(fComp (Hom A)) #) is strict CatStr
F2 is Element of the carrier' of (A)
cod F2 is Element of the carrier of (A)
the Target of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
K33( the carrier' of (A), the carrier of (A)) is Relation-like set
K32(K33( the carrier' of (A), the carrier of (A))) is set
the Target of (A) . F2 is Element of the carrier of (A)
(fCod (Hom A)) . F2 is set
t is Element of Maps (Hom A)
cod t is Element of Hom A
F2 `1 is set
(F2 `1) `2 is set
[(Hom ((cod F),F1)),(Hom ((dom F),F1))] `2 is set
the carrier of (Ens (Hom A)) is non empty set
hom?- ((Hom A),(dom F)) is non empty Relation-like the carrier' of A -defined the carrier' of (Ens (Hom A)) -valued Function-like V17( the carrier' of A) quasi_total Functor of A, Ens (Hom A)
the carrier' of (Ens (Hom A)) is non empty set
Obj (hom?- ((Hom A),(dom F))) is non empty Relation-like the carrier of A -defined the carrier of (Ens (Hom A)) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Ens (Hom A))))
K33( the carrier of A, the carrier of (Ens (Hom A))) is Relation-like set
K32(K33( the carrier of A, the carrier of (Ens (Hom A)))) is set
(Obj (hom?- ((Hom A),(dom F)))) . F1 is Element of the carrier of (Ens (Hom A))
(hom?- ((Hom A),(dom F))) . F1 is Element of the carrier of (Ens (Hom A))
dom F2 is Element of the carrier of (A)
the Source of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
the Source of (A) . F2 is Element of the carrier of (A)
(fDom (Hom A)) . F2 is set
dom t is Element of Hom A
(F2 `1) `1 is set
[(Hom ((cod F),F1)),(Hom ((dom F),F1))] `1 is set
hom?- ((Hom A),(cod F)) is non empty Relation-like the carrier' of A -defined the carrier' of (Ens (Hom A)) -valued Function-like V17( the carrier' of A) quasi_total Functor of A, Ens (Hom A)
Obj (hom?- ((Hom A),(cod F))) is non empty Relation-like the carrier of A -defined the carrier of (Ens (Hom A)) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Ens (Hom A))))
(Obj (hom?- ((Hom A),(cod F)))) . F1 is Element of the carrier of (Ens (Hom A))
(hom?- ((Hom A),(cod F))) . F1 is Element of the carrier of (Ens (Hom A))
F1 is Element of the carrier of A
Hom ((cod F),F1) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod F & cod b<sub>1</sub> = F1 ) } is set
Hom ((dom F),F1) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom F & cod b<sub>1</sub> = F1 ) } is set
[(Hom ((cod F),F1)),(Hom ((dom F),F1))] is V1() set
{(Hom ((cod F),F1)),(Hom ((dom F),F1))} is non empty set
{(Hom ((cod F),F1))} is non empty set
{{(Hom ((cod F),F1)),(Hom ((dom F),F1))},{(Hom ((cod F),F1))}} is non empty set
hom (F,F1) is Relation-like Hom ((cod F),F1) -defined Hom ((dom F),F1) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),F1)),(Hom ((dom F),F1))))
K33((Hom ((cod F),F1)),(Hom ((dom F),F1))) is Relation-like set
K32(K33((Hom ((cod F),F1)),(Hom ((dom F),F1)))) is set
[[(Hom ((cod F),F1)),(Hom ((dom F),F1))],(hom (F,F1))] is V1() set
{[(Hom ((cod F),F1)),(Hom ((dom F),F1))],(hom (F,F1))} is non empty set
{[(Hom ((cod F),F1)),(Hom ((dom F),F1))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),F1)),(Hom ((dom F),F1))],(hom (F,F1))},{[(Hom ((cod F),F1)),(Hom ((dom F),F1))]}} is non empty set
(A,(cod F)) . F1 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . F1 is Element of the carrier of (A)
(A,(dom F)) . F1 is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . F1 is Element of the carrier of (A)
Hom (((A,(cod F)) . F1),((A,(dom F)) . F1)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,(cod F)) . F1 & cod b<sub>1</sub> = (A,(dom F)) . F1 ) } is set
K33( the carrier of A, the carrier' of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier' of (A))) is set
F1 is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier' of (A)))
F2 is Element of the carrier of A
F1 . F2 is Element of the carrier' of (A)
(A,(cod F)) . F2 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . F2 is Element of the carrier of (A)
(A,(dom F)) . F2 is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . F2 is Element of the carrier of (A)
Hom ((cod F),F2) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod F & cod b<sub>1</sub> = F2 ) } is set
Hom ((dom F),F2) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom F & cod b<sub>1</sub> = F2 ) } is set
[(Hom ((cod F),F2)),(Hom ((dom F),F2))] is V1() set
{(Hom ((cod F),F2)),(Hom ((dom F),F2))} is non empty set
{(Hom ((cod F),F2))} is non empty set
{{(Hom ((cod F),F2)),(Hom ((dom F),F2))},{(Hom ((cod F),F2))}} is non empty set
hom (F,F2) is Relation-like Hom ((cod F),F2) -defined Hom ((dom F),F2) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),F2)),(Hom ((dom F),F2))))
K33((Hom ((cod F),F2)),(Hom ((dom F),F2))) is Relation-like set
K32(K33((Hom ((cod F),F2)),(Hom ((dom F),F2)))) is set
[[(Hom ((cod F),F2)),(Hom ((dom F),F2))],(hom (F,F2))] is V1() set
{[(Hom ((cod F),F2)),(Hom ((dom F),F2))],(hom (F,F2))} is non empty set
{[(Hom ((cod F),F2)),(Hom ((dom F),F2))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),F2)),(Hom ((dom F),F2))],(hom (F,F2))},{[(Hom ((cod F),F2)),(Hom ((dom F),F2))]}} is non empty set
Hom (((A,(cod F)) . F2),((A,(dom F)) . F2)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,(cod F)) . F2 & cod b<sub>1</sub> = (A,(dom F)) . F2 ) } is set
F2 is Element of the carrier of A
(A,(cod F)) . F2 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . F2 is Element of the carrier of (A)
(A,(dom F)) . F2 is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . F2 is Element of the carrier of (A)
Hom (((A,(cod F)) . F2),((A,(dom F)) . F2)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,(cod F)) . F2 & cod b<sub>1</sub> = (A,(dom F)) . F2 ) } is set
F2 is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total transformation of (A,(cod F)),(A,(dom F))
t is Element of the carrier of A
d1 is Element of the carrier of A
Hom (t,d1) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = t & cod b<sub>1</sub> = d1 ) } is set
(A,(cod F)) . t is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . t is Element of the carrier of (A)
(A,(cod F)) . d1 is Element of the carrier of (A)
(Obj (A,(cod F))) . d1 is Element of the carrier of (A)
(A,(dom F)) . d1 is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . d1 is Element of the carrier of (A)
F2 . d1 is Morphism of (A,(cod F)) . d1,(A,(dom F)) . d1
(A,(dom F)) . t is Element of the carrier of (A)
(Obj (A,(dom F))) . t is Element of the carrier of (A)
F2 . t is Morphism of (A,(cod F)) . t,(A,(dom F)) . t
Hom (((A,(cod F)) . t),((A,(cod F)) . d1)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,(cod F)) . t & cod b<sub>1</sub> = (A,(cod F)) . d1 ) } is set
d is Morphism of t,d1
(A,(cod F)) /. d is Morphism of (A,(cod F)) . t,(A,(cod F)) . d1
(F2 . d1) * ((A,(cod F)) /. d) is Morphism of (A,(cod F)) . t,(A,(dom F)) . d1
(A,(dom F)) /. d is Morphism of (A,(dom F)) . t,(A,(dom F)) . d1
((A,(dom F)) /. d) * (F2 . t) is Morphism of (A,(cod F)) . t,(A,(dom F)) . d1
dom d is Element of the carrier of A
the Source of A . d is Element of the carrier of A
hom ((cod F),d) is Relation-like Hom ((cod F),(dom d)) -defined Hom ((cod F),(cod d)) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))))
Hom ((cod F),(dom d)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod F & cod b<sub>1</sub> = dom d ) } is set
cod d is Element of the carrier of A
the Target of A . d is Element of the carrier of A
Hom ((cod F),(cod d)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod F & cod b<sub>1</sub> = cod d ) } is set
K33((Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))) is Relation-like set
K32(K33((Hom ((cod F),(dom d))),(Hom ((cod F),(cod d))))) is set
proj2 (hom ((cod F),d)) is set
hom (F,d1) is Relation-like Hom ((cod F),d1) -defined Hom ((dom F),d1) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),d1)),(Hom ((dom F),d1))))
Hom ((cod F),d1) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod F & cod b<sub>1</sub> = d1 ) } is set
Hom ((dom F),d1) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom F & cod b<sub>1</sub> = d1 ) } is set
K33((Hom ((cod F),d1)),(Hom ((dom F),d1))) is Relation-like set
K32(K33((Hom ((cod F),d1)),(Hom ((dom F),d1)))) is set
proj1 (hom (F,d1)) is set
t is set
hom (F,t) is Relation-like Hom ((cod F),t) -defined Hom ((dom F),t) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),t)),(Hom ((dom F),t))))
Hom ((cod F),t) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod F & cod b<sub>1</sub> = t ) } is set
Hom ((dom F),t) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom F & cod b<sub>1</sub> = t ) } is set
K33((Hom ((cod F),t)),(Hom ((dom F),t))) is Relation-like set
K32(K33((Hom ((cod F),t)),(Hom ((dom F),t)))) is set
proj2 (hom (F,t)) is set
hom ((dom F),d) is Relation-like Hom ((dom F),(dom d)) -defined Hom ((dom F),(cod d)) -valued Function-like quasi_total Element of K32(K33((Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))))
Hom ((dom F),(dom d)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom F & cod b<sub>1</sub> = dom d ) } is set
Hom ((dom F),(cod d)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom F & cod b<sub>1</sub> = cod d ) } is set
K33((Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))) is Relation-like set
K32(K33((Hom ((dom F),(dom d))),(Hom ((dom F),(cod d))))) is set
proj1 (hom ((dom F),d)) is set
t is set
(hom ((cod F),d)) * (hom (F,d1)) is Relation-like Hom ((cod F),(dom d)) -defined Hom ((dom F),d1) -valued Function-like set
proj1 ((hom ((cod F),d)) * (hom (F,d1))) is set
(hom (F,t)) * (hom ((dom F),d)) is Relation-like Hom ((cod F),t) -defined Hom ((dom F),(cod d)) -valued Function-like set
proj1 ((hom (F,t)) * (hom ((dom F),d))) is set
proj1 (hom ((cod F),d)) is set
proj1 (hom (F,t)) is set
proj1 (hom ((cod F),d)) is set
proj1 (hom (F,t)) is set
t is set
((hom ((cod F),d)) * (hom (F,d1))) . t is set
((hom (F,t)) * (hom ((dom F),d))) . t is set
proj1 (hom ((cod F),d)) is set
t1 is Element of the carrier' of A
cod t1 is Element of the carrier of A
the Target of A . t1 is Element of the carrier of A
dom t1 is Element of the carrier of A
the Source of A . t1 is Element of the carrier of A
d (*) t1 is Element of the carrier' of A
cod (d (*) t1) is Element of the carrier of A
the Target of A . (d (*) t1) is Element of the carrier of A
(hom (F,t)) . t1 is set
t1 (*) F is Element of the carrier' of A
dom (t1 (*) F) is Element of the carrier of A
the Source of A . (t1 (*) F) is Element of the carrier of A
dom (d (*) t1) is Element of the carrier of A
the Source of A . (d (*) t1) is Element of the carrier of A
cod (t1 (*) F) is Element of the carrier of A
the Target of A . (t1 (*) F) is Element of the carrier of A
((hom ((cod F),d)) * (hom (F,d1))) . t1 is set
(hom ((cod F),d)) . t1 is set
(hom (F,d1)) . ((hom ((cod F),d)) . t1) is set
(hom (F,d1)) . (d (*) t1) is set
(d (*) t1) (*) F is Element of the carrier' of A
d (*) (t1 (*) F) is Element of the carrier' of A
f is Element of the carrier' of A
d (*) f is Element of the carrier' of A
(hom ((dom F),d)) . ((hom (F,t)) . t1) is set
((hom (F,t)) * (hom ((dom F),d))) . t1 is set
proj1 (hom ((cod F),d)) is set
Hom (((A,(dom F)) . t),((A,(dom F)) . d1)) is Element of K32( the carrier' of (A))
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,(dom F)) . t & cod b<sub>1</sub> = (A,(dom F)) . d1 ) } is set
F2 . t is Element of the carrier' of (A)
[(Hom ((cod F),t)),(Hom ((dom F),t))] is V1() set
{(Hom ((cod F),t)),(Hom ((dom F),t))} is non empty set
{(Hom ((cod F),t))} is non empty set
{{(Hom ((cod F),t)),(Hom ((dom F),t))},{(Hom ((cod F),t))}} is non empty set
[[(Hom ((cod F),t)),(Hom ((dom F),t))],(hom (F,t))] is V1() set
{[(Hom ((cod F),t)),(Hom ((dom F),t))],(hom (F,t))} is non empty set
{[(Hom ((cod F),t)),(Hom ((dom F),t))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),t)),(Hom ((dom F),t))],(hom (F,t))},{[(Hom ((cod F),t)),(Hom ((dom F),t))]}} is non empty set
t is Element of the carrier' of (A)
Hom (((A,(cod F)) . t),((A,(dom F)) . t)) is Element of K32( the carrier' of (A))
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,(cod F)) . t & cod b<sub>1</sub> = (A,(dom F)) . t ) } is set
F2 . d1 is Element of the carrier' of (A)
[(Hom ((cod F),d1)),(Hom ((dom F),d1))] is V1() set
{(Hom ((cod F),d1)),(Hom ((dom F),d1))} is non empty set
{(Hom ((cod F),d1))} is non empty set
{{(Hom ((cod F),d1)),(Hom ((dom F),d1))},{(Hom ((cod F),d1))}} is non empty set
[[(Hom ((cod F),d1)),(Hom ((dom F),d1))],(hom (F,d1))] is V1() set
{[(Hom ((cod F),d1)),(Hom ((dom F),d1))],(hom (F,d1))} is non empty set
{[(Hom ((cod F),d1)),(Hom ((dom F),d1))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),d1)),(Hom ((dom F),d1))],(hom (F,d1))},{[(Hom ((cod F),d1)),(Hom ((dom F),d1))]}} is non empty set
f is Element of the carrier' of (A)
fDom (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
K33((Maps (Hom A)),(Hom A)) is Relation-like set
K32(K33((Maps (Hom A)),(Hom A))) is set
fCod (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
fComp (Hom A) is Relation-like K33((Maps (Hom A)),(Maps (Hom A))) -defined Maps (Hom A) -valued Function-like Element of K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))))
K33((Maps (Hom A)),(Maps (Hom A))) is Relation-like set
K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))) is Relation-like set
K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A)))) is set
CatStr(# (Hom A),(Maps (Hom A)),(fDom (Hom A)),(fCod (Hom A)),(fComp (Hom A)) #) is strict CatStr
cod f is Element of the carrier of (A)
the Target of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
K33( the carrier' of (A), the carrier of (A)) is Relation-like set
K32(K33( the carrier' of (A), the carrier of (A))) is set
the Target of (A) . f is Element of the carrier of (A)
(fCod (Hom A)) . f is set
a is Element of Maps (Hom A)
cod a is Element of Hom A
f `1 is set
(f `1) `2 is set
[(Hom ((cod F),d1)),(Hom ((dom F),d1))] `2 is set
dom t is Element of the carrier of (A)
the Source of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
the Source of (A) . t is Element of the carrier of (A)
(fDom (Hom A)) . t is set
t1 is Element of Maps (Hom A)
dom t1 is Element of Hom A
t `1 is set
(t `1) `1 is set
[(Hom ((cod F),t)),(Hom ((dom F),t))] `1 is set
cod t is Element of the carrier of (A)
the Target of (A) . t is Element of the carrier of (A)
(fCod (Hom A)) . t is set
cod t1 is Element of Hom A
(t `1) `2 is set
[(Hom ((cod F),t)),(Hom ((dom F),t))] `2 is set
ta1 is Element of the carrier' of (A)
(hom?- (cod F)) . d is Element of Maps (Hom A)
[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))] is V1() set
{(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))} is non empty set
{(Hom ((cod F),(dom d)))} is non empty set
{{(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))},{(Hom ((cod F),(dom d)))}} is non empty set
[[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))],(hom ((cod F),d))] is V1() set
{[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))],(hom ((cod F),d))} is non empty set
{[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))],(hom ((cod F),d))},{[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))]}} is non empty set
dom ta1 is Element of the carrier of (A)
the Source of (A) . ta1 is Element of the carrier of (A)
(fDom (Hom A)) . ta1 is set
X is Element of Maps (Hom A)
dom X is Element of Hom A
ta1 `1 is set
(ta1 `1) `1 is set
[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))] `1 is set
cod ta1 is Element of the carrier of (A)
the Target of (A) . ta1 is Element of the carrier of (A)
(fCod (Hom A)) . ta1 is set
cod X is Element of Hom A
(ta1 `1) `2 is set
[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))] `2 is set
dom f is Element of the carrier of (A)
the Source of (A) . f is Element of the carrier of (A)
(fDom (Hom A)) . f is set
dom a is Element of Hom A
(f `1) `1 is set
[(Hom ((cod F),d1)),(Hom ((dom F),d1))] `1 is set
t1 is Element of the carrier' of (A)
(hom?- (dom F)) . d is Element of Maps (Hom A)
[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))] is V1() set
{(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))} is non empty set
{(Hom ((dom F),(dom d)))} is non empty set
{{(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))},{(Hom ((dom F),(dom d)))}} is non empty set
[[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))],(hom ((dom F),d))] is V1() set
{[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))],(hom ((dom F),d))} is non empty set
{[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))]} is non empty Relation-like Function-like set
{{[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))],(hom ((dom F),d))},{[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))]}} is non empty set
cod t1 is Element of the carrier of (A)
the Target of (A) . t1 is Element of the carrier of (A)
(fCod (Hom A)) . t1 is set
x is Element of Maps (Hom A)
cod x is Element of Hom A
t1 `1 is set
(t1 `1) `2 is set
[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))] `2 is set
dom t1 is Element of the carrier of (A)
the Source of (A) . t1 is Element of the carrier of (A)
(fDom (Hom A)) . t1 is set
dom x is Element of Hom A
(t1 `1) `1 is set
[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))] `1 is set
Hom (((A,(cod F)) . d1),((A,(dom F)) . d1)) is Element of K32( the carrier' of (A))
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,(cod F)) . d1 & cod b<sub>1</sub> = (A,(dom F)) . d1 ) } is set
f (*) ta1 is Element of the carrier' of (A)
[(Hom ((cod F),(dom d))),(Hom ((dom F),d1))] is V1() set
{(Hom ((cod F),(dom d))),(Hom ((dom F),d1))} is non empty set
{{(Hom ((cod F),(dom d))),(Hom ((dom F),d1))},{(Hom ((cod F),(dom d)))}} is non empty set
[[(Hom ((cod F),(dom d))),(Hom ((dom F),d1))],((hom ((cod F),d)) * (hom (F,d1)))] is V1() set
{[(Hom ((cod F),(dom d))),(Hom ((dom F),d1))],((hom ((cod F),d)) * (hom (F,d1)))} is non empty set
{[(Hom ((cod F),(dom d))),(Hom ((dom F),d1))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),(dom d))),(Hom ((dom F),d1))],((hom ((cod F),d)) * (hom (F,d1)))},{[(Hom ((cod F),(dom d))),(Hom ((dom F),d1))]}} is non empty set
[(Hom ((cod F),t)),(Hom ((dom F),(cod d)))] is V1() set
{(Hom ((cod F),t)),(Hom ((dom F),(cod d)))} is non empty set
{{(Hom ((cod F),t)),(Hom ((dom F),(cod d)))},{(Hom ((cod F),t))}} is non empty set
[[(Hom ((cod F),t)),(Hom ((dom F),(cod d)))],((hom (F,t)) * (hom ((dom F),d)))] is V1() set
{[(Hom ((cod F),t)),(Hom ((dom F),(cod d)))],((hom (F,t)) * (hom ((dom F),d)))} is non empty set
{[(Hom ((cod F),t)),(Hom ((dom F),(cod d)))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),t)),(Hom ((dom F),(cod d)))],((hom (F,t)) * (hom ((dom F),d)))},{[(Hom ((cod F),t)),(Hom ((dom F),(cod d)))]}} is non empty set
t1 (*) t is Element of the carrier' of (A)
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
(A) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Hom A is non empty set
Ens (Hom A) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (A) is non empty set
F is Element of the carrier' of A
cod F is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Target of A . F is Element of the carrier of A
(A,(cod F)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod F) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
Maps (Hom A) is non empty set
K33( the carrier' of A,(Maps (Hom A))) is Relation-like set
K32(K33( the carrier' of A,(Maps (Hom A)))) is set
dom F is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Source of A . F is Element of the carrier of A
(A,(dom F)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom F) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
F1 is Element of the carrier of A
Hom ((cod F),F1) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod F & cod b<sub>1</sub> = F1 ) } is set
Hom ((dom F),F1) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom F & cod b<sub>1</sub> = F1 ) } is set
[(Hom ((cod F),F1)),(Hom ((dom F),F1))] is V1() set
{(Hom ((cod F),F1)),(Hom ((dom F),F1))} is non empty set
{(Hom ((cod F),F1))} is non empty set
{{(Hom ((cod F),F1)),(Hom ((dom F),F1))},{(Hom ((cod F),F1))}} is non empty set
id F1 is Morphism of F1,F1
hom (F,(id F1)) is Relation-like Hom ((cod F),(dom (id F1))) -defined Hom ((dom F),(cod (id F1))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),(dom (id F1)))),(Hom ((dom F),(cod (id F1))))))
dom (id F1) is Element of the carrier of A
the Source of A . (id F1) is Element of the carrier of A
Hom ((cod F),(dom (id F1))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod F & cod b<sub>1</sub> = dom (id F1) ) } is set
cod (id F1) is Element of the carrier of A
the Target of A . (id F1) is Element of the carrier of A
Hom ((dom F),(cod (id F1))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom F & cod b<sub>1</sub> = cod (id F1) ) } is set
K33((Hom ((cod F),(dom (id F1)))),(Hom ((dom F),(cod (id F1))))) is Relation-like set
K32(K33((Hom ((cod F),(dom (id F1)))),(Hom ((dom F),(cod (id F1)))))) is set
[[(Hom ((cod F),F1)),(Hom ((dom F),F1))],(hom (F,(id F1)))] is V1() set
{[(Hom ((cod F),F1)),(Hom ((dom F),F1))],(hom (F,(id F1)))} is non empty set
{[(Hom ((cod F),F1)),(Hom ((dom F),F1))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),F1)),(Hom ((dom F),F1))],(hom (F,(id F1)))},{[(Hom ((cod F),F1)),(Hom ((dom F),F1))]}} is non empty set
(A,(cod F)) . F1 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . F1 is Element of the carrier of (A)
(A,(dom F)) . F1 is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . F1 is Element of the carrier of (A)
Hom (((A,(cod F)) . F1),((A,(dom F)) . F1)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,(cod F)) . F1 & cod b<sub>1</sub> = (A,(dom F)) . F1 ) } is set
fDom (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
K33((Maps (Hom A)),(Hom A)) is Relation-like set
K32(K33((Maps (Hom A)),(Hom A))) is set
fCod (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
fComp (Hom A) is Relation-like K33((Maps (Hom A)),(Maps (Hom A))) -defined Maps (Hom A) -valued Function-like Element of K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))))
K33((Maps (Hom A)),(Maps (Hom A))) is Relation-like set
K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))) is Relation-like set
K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A)))) is set
CatStr(# (Hom A),(Maps (Hom A)),(fDom (Hom A)),(fCod (Hom A)),(fComp (Hom A)) #) is strict CatStr
hom (F,F1) is Relation-like Hom ((cod F),F1) -defined Hom ((dom F),F1) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),F1)),(Hom ((dom F),F1))))
K33((Hom ((cod F),F1)),(Hom ((dom F),F1))) is Relation-like set
K32(K33((Hom ((cod F),F1)),(Hom ((dom F),F1)))) is set
F2 is Element of the carrier' of (A)
cod F2 is Element of the carrier of (A)
the Target of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
K33( the carrier' of (A), the carrier of (A)) is Relation-like set
K32(K33( the carrier' of (A), the carrier of (A))) is set
the Target of (A) . F2 is Element of the carrier of (A)
(fCod (Hom A)) . F2 is set
t is Element of Maps (Hom A)
cod t is Element of Hom A
F2 `1 is set
(F2 `1) `2 is set
[(Hom ((cod F),F1)),(Hom ((dom F),F1))] `2 is set
the carrier of (Ens (Hom A)) is non empty set
hom?- ((Hom A),(dom F)) is non empty Relation-like the carrier' of A -defined the carrier' of (Ens (Hom A)) -valued Function-like V17( the carrier' of A) quasi_total Functor of A, Ens (Hom A)
the carrier' of (Ens (Hom A)) is non empty set
Obj (hom?- ((Hom A),(dom F))) is non empty Relation-like the carrier of A -defined the carrier of (Ens (Hom A)) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Ens (Hom A))))
K33( the carrier of A, the carrier of (Ens (Hom A))) is Relation-like set
K32(K33( the carrier of A, the carrier of (Ens (Hom A)))) is set
(Obj (hom?- ((Hom A),(dom F)))) . F1 is Element of the carrier of (Ens (Hom A))
(hom?- ((Hom A),(dom F))) . F1 is Element of the carrier of (Ens (Hom A))
dom F2 is Element of the carrier of (A)
the Source of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
the Source of (A) . F2 is Element of the carrier of (A)
(fDom (Hom A)) . F2 is set
dom t is Element of Hom A
(F2 `1) `1 is set
[(Hom ((cod F),F1)),(Hom ((dom F),F1))] `1 is set
hom?- ((Hom A),(cod F)) is non empty Relation-like the carrier' of A -defined the carrier' of (Ens (Hom A)) -valued Function-like V17( the carrier' of A) quasi_total Functor of A, Ens (Hom A)
Obj (hom?- ((Hom A),(cod F))) is non empty Relation-like the carrier of A -defined the carrier of (Ens (Hom A)) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Ens (Hom A))))
(Obj (hom?- ((Hom A),(cod F)))) . F1 is Element of the carrier of (Ens (Hom A))
(hom?- ((Hom A),(cod F))) . F1 is Element of the carrier of (Ens (Hom A))
F1 is Element of the carrier of A
Hom ((cod F),F1) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = F1 ) } is set
Hom ((dom F),F1) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = F1 ) } is set
[(Hom ((cod F),F1)),(Hom ((dom F),F1))] is V1() set
{(Hom ((cod F),F1)),(Hom ((dom F),F1))} is non empty set
{(Hom ((cod F),F1))} is non empty set
{{(Hom ((cod F),F1)),(Hom ((dom F),F1))},{(Hom ((cod F),F1))}} is non empty set
id F1 is Morphism of F1,F1
hom (F,(id F1)) is Relation-like Hom ((cod F),(dom (id F1))) -defined Hom ((dom F),(cod (id F1))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),(dom (id F1)))),(Hom ((dom F),(cod (id F1))))))
dom (id F1) is Element of the carrier of A
the Source of A . (id F1) is Element of the carrier of A
Hom ((cod F),(dom (id F1))) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = dom (id F1) ) } is set
cod (id F1) is Element of the carrier of A
the Target of A . (id F1) is Element of the carrier of A
Hom ((dom F),(cod (id F1))) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = cod (id F1) ) } is set
K33((Hom ((cod F),(dom (id F1)))),(Hom ((dom F),(cod (id F1))))) is Relation-like set
K32(K33((Hom ((cod F),(dom (id F1)))),(Hom ((dom F),(cod (id F1)))))) is set
[[(Hom ((cod F),F1)),(Hom ((dom F),F1))],(hom (F,(id F1)))] is V1() set
{[(Hom ((cod F),F1)),(Hom ((dom F),F1))],(hom (F,(id F1)))} is non empty set
{[(Hom ((cod F),F1)),(Hom ((dom F),F1))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),F1)),(Hom ((dom F),F1))],(hom (F,(id F1)))},{[(Hom ((cod F),F1)),(Hom ((dom F),F1))]}} is non empty set
(A,(cod F)) . F1 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . F1 is Element of the carrier of (A)
(A,(dom F)) . F1 is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . F1 is Element of the carrier of (A)
Hom (((A,(cod F)) . F1),((A,(dom F)) . F1)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b₁ where b₁ is Element of the carrier' of (A) : ( dom b₁ = (A,(cod F)) . F1 & cod b₁ = (A,(dom F)) . F1 ) } is set
K33( the carrier of A, the carrier' of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier' of (A))) is set
F1 is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier' of (A)))
F2 is Element of the carrier of A
F1 . F2 is Element of the carrier' of (A)
(A,(cod F)) . F2 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . F2 is Element of the carrier of (A)
(A,(dom F)) . F2 is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . F2 is Element of the carrier of (A)
Hom ((cod F),F2) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = F2 ) } is set
Hom ((dom F),F2) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = F2 ) } is set
[(Hom ((cod F),F2)),(Hom ((dom F),F2))] is V1() set
{(Hom ((cod F),F2)),(Hom ((dom F),F2))} is non empty set
{(Hom ((cod F),F2))} is non empty set
{{(Hom ((cod F),F2)),(Hom ((dom F),F2))},{(Hom ((cod F),F2))}} is non empty set
id F2 is Morphism of F2,F2
hom (F,(id F2)) is Relation-like Hom ((cod F),(dom (id F2))) -defined Hom ((dom F),(cod (id F2))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),(dom (id F2)))),(Hom ((dom F),(cod (id F2))))))
dom (id F2) is Element of the carrier of A
the Source of A . (id F2) is Element of the carrier of A
Hom ((cod F),(dom (id F2))) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = dom (id F2) ) } is set
cod (id F2) is Element of the carrier of A
the Target of A . (id F2) is Element of the carrier of A
Hom ((dom F),(cod (id F2))) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = cod (id F2) ) } is set
K33((Hom ((cod F),(dom (id F2)))),(Hom ((dom F),(cod (id F2))))) is Relation-like set
K32(K33((Hom ((cod F),(dom (id F2)))),(Hom ((dom F),(cod (id F2)))))) is set
[[(Hom ((cod F),F2)),(Hom ((dom F),F2))],(hom (F,(id F2)))] is V1() set
{[(Hom ((cod F),F2)),(Hom ((dom F),F2))],(hom (F,(id F2)))} is non empty set
{[(Hom ((cod F),F2)),(Hom ((dom F),F2))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),F2)),(Hom ((dom F),F2))],(hom (F,(id F2)))},{[(Hom ((cod F),F2)),(Hom ((dom F),F2))]}} is non empty set
Hom (((A,(cod F)) . F2),((A,(dom F)) . F2)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b₁ where b₁ is Element of the carrier' of (A) : ( dom b₁ = (A,(cod F)) . F2 & cod b₁ = (A,(dom F)) . F2 ) } is set
F2 is Element of the carrier of A
(A,(cod F)) . F2 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . F2 is Element of the carrier of (A)
(A,(dom F)) . F2 is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . F2 is Element of the carrier of (A)
Hom (((A,(cod F)) . F2),((A,(dom F)) . F2)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b₁ where b₁ is Element of the carrier' of (A) : ( dom b₁ = (A,(cod F)) . F2 & cod b₁ = (A,(dom F)) . F2 ) } is set
F2 is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total transformation of (A,(cod F)),(A,(dom F))
t is Element of the carrier of A
d1 is Element of the carrier of A
Hom (t,d1) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = t & cod b₁ = d1 ) } is set
(A,(cod F)) . t is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . t is Element of the carrier of (A)
(A,(cod F)) . d1 is Element of the carrier of (A)
(Obj (A,(cod F))) . d1 is Element of the carrier of (A)
(A,(dom F)) . d1 is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . d1 is Element of the carrier of (A)
F2 . d1 is Morphism of (A,(cod F)) . d1,(A,(dom F)) . d1
(A,(dom F)) . t is Element of the carrier of (A)
(Obj (A,(dom F))) . t is Element of the carrier of (A)
F2 . t is Morphism of (A,(cod F)) . t,(A,(dom F)) . t
Hom (((A,(cod F)) . t),((A,(cod F)) . d1)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b₁ where b₁ is Element of the carrier' of (A) : ( dom b₁ = (A,(cod F)) . t & cod b₁ = (A,(cod F)) . d1 ) } is set
d is Morphism of t,d1
(A,(cod F)) /. d is Morphism of (A,(cod F)) . t,(A,(cod F)) . d1
(F2 . d1) * ((A,(cod F)) /. d) is Morphism of (A,(cod F)) . t,(A,(dom F)) . d1
(A,(dom F)) /. d is Morphism of (A,(dom F)) . t,(A,(dom F)) . d1
((A,(dom F)) /. d) * (F2 . t) is Morphism of (A,(cod F)) . t,(A,(dom F)) . d1
dom d is Element of the carrier of A
the Source of A . d is Element of the carrier of A
hom ((cod F),d) is Relation-like Hom ((cod F),(dom d)) -defined Hom ((cod F),(cod d)) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))))
Hom ((cod F),(dom d)) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = dom d ) } is set
cod d is Element of the carrier of A
the Target of A . d is Element of the carrier of A
Hom ((cod F),(cod d)) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = cod d ) } is set
K33((Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))) is Relation-like set
K32(K33((Hom ((cod F),(dom d))),(Hom ((cod F),(cod d))))) is set
proj2 (hom ((cod F),d)) is set
hom (F,d1) is Relation-like Hom ((cod F),d1) -defined Hom ((dom F),d1) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),d1)),(Hom ((dom F),d1))))
Hom ((cod F),d1) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = d1 ) } is set
Hom ((dom F),d1) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = d1 ) } is set
K33((Hom ((cod F),d1)),(Hom ((dom F),d1))) is Relation-like set
K32(K33((Hom ((cod F),d1)),(Hom ((dom F),d1)))) is set
proj1 (hom (F,d1)) is set
t is set
hom (F,t) is Relation-like Hom ((cod F),t) -defined Hom ((dom F),t) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),t)),(Hom ((dom F),t))))
Hom ((cod F),t) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = t ) } is set
Hom ((dom F),t) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = t ) } is set
K33((Hom ((cod F),t)),(Hom ((dom F),t))) is Relation-like set
K32(K33((Hom ((cod F),t)),(Hom ((dom F),t)))) is set
proj2 (hom (F,t)) is set
hom ((dom F),d) is Relation-like Hom ((dom F),(dom d)) -defined Hom ((dom F),(cod d)) -valued Function-like quasi_total Element of K32(K33((Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))))
Hom ((dom F),(dom d)) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = dom d ) } is set
Hom ((dom F),(cod d)) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = cod d ) } is set
K33((Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))) is Relation-like set
K32(K33((Hom ((dom F),(dom d))),(Hom ((dom F),(cod d))))) is set
proj1 (hom ((dom F),d)) is set
t is set
(hom ((cod F),d)) * (hom (F,d1)) is Relation-like Hom ((cod F),(dom d)) -defined Hom ((dom F),d1) -valued Function-like set
proj1 ((hom ((cod F),d)) * (hom (F,d1))) is set
(hom (F,t)) * (hom ((dom F),d)) is Relation-like Hom ((cod F),t) -defined Hom ((dom F),(cod d)) -valued Function-like set
proj1 ((hom (F,t)) * (hom ((dom F),d))) is set
proj1 (hom ((cod F),d)) is set
proj1 (hom (F,t)) is set
proj1 (hom ((cod F),d)) is set
proj1 (hom (F,t)) is set
t is set
((hom ((cod F),d)) * (hom (F,d1))) . t is set
((hom (F,t)) * (hom ((dom F),d))) . t is set
proj1 (hom ((cod F),d)) is set
t1 is Element of the carrier' of A
cod t1 is Element of the carrier of A
the Target of A . t1 is Element of the carrier of A
d (*) t1 is Element of the carrier' of A
cod (d (*) t1) is Element of the carrier of A
the Target of A . (d (*) t1) is Element of the carrier of A
dom (d (*) t1) is Element of the carrier of A
the Source of A . (d (*) t1) is Element of the carrier of A
dom t1 is Element of the carrier of A
the Source of A . t1 is Element of the carrier of A
t1 (*) F is Element of the carrier' of A
dom (t1 (*) F) is Element of the carrier of A
the Source of A . (t1 (*) F) is Element of the carrier of A
(hom (F,t)) . t1 is set
cod (t1 (*) F) is Element of the carrier of A
the Target of A . (t1 (*) F) is Element of the carrier of A
((hom ((cod F),d)) * (hom (F,d1))) . t1 is set
(hom ((cod F),d)) . t1 is set
(hom (F,d1)) . ((hom ((cod F),d)) . t1) is set
(hom (F,d1)) . (d (*) t1) is set
(d (*) t1) (*) F is Element of the carrier' of A
d (*) (t1 (*) F) is Element of the carrier' of A
f is Element of the carrier' of A
d (*) f is Element of the carrier' of A
(hom ((dom F),d)) . ((hom (F,t)) . t1) is set
((hom (F,t)) * (hom ((dom F),d))) . t1 is set
proj1 (hom ((cod F),d)) is set
Hom (((A,(dom F)) . t),((A,(dom F)) . d1)) is Element of K32( the carrier' of (A))
{ b₁ where b₁ is Element of the carrier' of (A) : ( dom b₁ = (A,(dom F)) . t & cod b₁ = (A,(dom F)) . d1 ) } is set
F2 . t is Element of the carrier' of (A)
[(Hom ((cod F),t)),(Hom ((dom F),t))] is V1() set
{(Hom ((cod F),t)),(Hom ((dom F),t))} is non empty set
{(Hom ((cod F),t))} is non empty set
{{(Hom ((cod F),t)),(Hom ((dom F),t))},{(Hom ((cod F),t))}} is non empty set
id t is Morphism of t,t
hom (F,(id t)) is Relation-like Hom ((cod F),(dom (id t))) -defined Hom ((dom F),(cod (id t))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),(dom (id t)))),(Hom ((dom F),(cod (id t))))))
dom (id t) is Element of the carrier of A
the Source of A . (id t) is Element of the carrier of A
Hom ((cod F),(dom (id t))) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = dom (id t) ) } is set
cod (id t) is Element of the carrier of A
the Target of A . (id t) is Element of the carrier of A
Hom ((dom F),(cod (id t))) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = cod (id t) ) } is set
K33((Hom ((cod F),(dom (id t)))),(Hom ((dom F),(cod (id t))))) is Relation-like set
K32(K33((Hom ((cod F),(dom (id t)))),(Hom ((dom F),(cod (id t)))))) is set
[[(Hom ((cod F),t)),(Hom ((dom F),t))],(hom (F,(id t)))] is V1() set
{[(Hom ((cod F),t)),(Hom ((dom F),t))],(hom (F,(id t)))} is non empty set
{[(Hom ((cod F),t)),(Hom ((dom F),t))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),t)),(Hom ((dom F),t))],(hom (F,(id t)))},{[(Hom ((cod F),t)),(Hom ((dom F),t))]}} is non empty set
[[(Hom ((cod F),t)),(Hom ((dom F),t))],(hom (F,t))] is V1() set
{[(Hom ((cod F),t)),(Hom ((dom F),t))],(hom (F,t))} is non empty set
{{[(Hom ((cod F),t)),(Hom ((dom F),t))],(hom (F,t))},{[(Hom ((cod F),t)),(Hom ((dom F),t))]}} is non empty set
t is Element of the carrier' of (A)
Hom (((A,(cod F)) . t),((A,(dom F)) . t)) is Element of K32( the carrier' of (A))
{ b₁ where b₁ is Element of the carrier' of (A) : ( dom b₁ = (A,(cod F)) . t & cod b₁ = (A,(dom F)) . t ) } is set
F2 . d1 is Element of the carrier' of (A)
[(Hom ((cod F),d1)),(Hom ((dom F),d1))] is V1() set
{(Hom ((cod F),d1)),(Hom ((dom F),d1))} is non empty set
{(Hom ((cod F),d1))} is non empty set
{{(Hom ((cod F),d1)),(Hom ((dom F),d1))},{(Hom ((cod F),d1))}} is non empty set
id d1 is Morphism of d1,d1
hom (F,(id d1)) is Relation-like Hom ((cod F),(dom (id d1))) -defined Hom ((dom F),(cod (id d1))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),(dom (id d1)))),(Hom ((dom F),(cod (id d1))))))
dom (id d1) is Element of the carrier of A
the Source of A . (id d1) is Element of the carrier of A
Hom ((cod F),(dom (id d1))) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = dom (id d1) ) } is set
cod (id d1) is Element of the carrier of A
the Target of A . (id d1) is Element of the carrier of A
Hom ((dom F),(cod (id d1))) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = cod (id d1) ) } is set
K33((Hom ((cod F),(dom (id d1)))),(Hom ((dom F),(cod (id d1))))) is Relation-like set
K32(K33((Hom ((cod F),(dom (id d1)))),(Hom ((dom F),(cod (id d1)))))) is set
[[(Hom ((cod F),d1)),(Hom ((dom F),d1))],(hom (F,(id d1)))] is V1() set
{[(Hom ((cod F),d1)),(Hom ((dom F),d1))],(hom (F,(id d1)))} is non empty set
{[(Hom ((cod F),d1)),(Hom ((dom F),d1))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),d1)),(Hom ((dom F),d1))],(hom (F,(id d1)))},{[(Hom ((cod F),d1)),(Hom ((dom F),d1))]}} is non empty set
[[(Hom ((cod F),d1)),(Hom ((dom F),d1))],(hom (F,d1))] is V1() set
{[(Hom ((cod F),d1)),(Hom ((dom F),d1))],(hom (F,d1))} is non empty set
{{[(Hom ((cod F),d1)),(Hom ((dom F),d1))],(hom (F,d1))},{[(Hom ((cod F),d1)),(Hom ((dom F),d1))]}} is non empty set
f is Element of the carrier' of (A)
fDom (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
K33((Maps (Hom A)),(Hom A)) is Relation-like set
K32(K33((Maps (Hom A)),(Hom A))) is set
fCod (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
fComp (Hom A) is Relation-like K33((Maps (Hom A)),(Maps (Hom A))) -defined Maps (Hom A) -valued Function-like Element of K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))))
K33((Maps (Hom A)),(Maps (Hom A))) is Relation-like set
K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))) is Relation-like set
K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A)))) is set
CatStr(# (Hom A),(Maps (Hom A)),(fDom (Hom A)),(fCod (Hom A)),(fComp (Hom A)) #) is strict CatStr
cod f is Element of the carrier of (A)
the Target of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
K33( the carrier' of (A), the carrier of (A)) is Relation-like set
K32(K33( the carrier' of (A), the carrier of (A))) is set
the Target of (A) . f is Element of the carrier of (A)
(fCod (Hom A)) . f is set
a is Element of Maps (Hom A)
cod a is Element of Hom A
f `1 is set
(f `1) `2 is set
[(Hom ((cod F),d1)),(Hom ((dom F),d1))] `2 is set
dom t is Element of the carrier of (A)
the Source of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
the Source of (A) . t is Element of the carrier of (A)
(fDom (Hom A)) . t is set
t1 is Element of Maps (Hom A)
dom t1 is Element of Hom A
t `1 is set
(t `1) `1 is set
[(Hom ((cod F),t)),(Hom ((dom F),t))] `1 is set
cod t is Element of the carrier of (A)
the Target of (A) . t is Element of the carrier of (A)
(fCod (Hom A)) . t is set
cod t1 is Element of Hom A
(t `1) `2 is set
[(Hom ((cod F),t)),(Hom ((dom F),t))] `2 is set
ta1 is Element of the carrier' of (A)
(hom?- (cod F)) . d is Element of Maps (Hom A)
[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))] is V1() set
{(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))} is non empty set
{(Hom ((cod F),(dom d)))} is non empty set
{{(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))},{(Hom ((cod F),(dom d)))}} is non empty set
[[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))],(hom ((cod F),d))] is V1() set
{[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))],(hom ((cod F),d))} is non empty set
{[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))],(hom ((cod F),d))},{[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))]}} is non empty set
dom ta1 is Element of the carrier of (A)
the Source of (A) . ta1 is Element of the carrier of (A)
(fDom (Hom A)) . ta1 is set
X is Element of Maps (Hom A)
dom X is Element of Hom A
ta1 `1 is set
(ta1 `1) `1 is set
[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))] `1 is set
cod ta1 is Element of the carrier of (A)
the Target of (A) . ta1 is Element of the carrier of (A)
(fCod (Hom A)) . ta1 is set
cod X is Element of Hom A
(ta1 `1) `2 is set
[(Hom ((cod F),(dom d))),(Hom ((cod F),(cod d)))] `2 is set
dom f is Element of the carrier of (A)
the Source of (A) . f is Element of the carrier of (A)
(fDom (Hom A)) . f is set
dom a is Element of Hom A
(f `1) `1 is set
[(Hom ((cod F),d1)),(Hom ((dom F),d1))] `1 is set
t1 is Element of the carrier' of (A)
(hom?- (dom F)) . d is Element of Maps (Hom A)
[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))] is V1() set
{(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))} is non empty set
{(Hom ((dom F),(dom d)))} is non empty set
{{(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))},{(Hom ((dom F),(dom d)))}} is non empty set
[[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))],(hom ((dom F),d))] is V1() set
{[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))],(hom ((dom F),d))} is non empty set
{[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))]} is non empty Relation-like Function-like set
{{[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))],(hom ((dom F),d))},{[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))]}} is non empty set
cod t1 is Element of the carrier of (A)
the Target of (A) . t1 is Element of the carrier of (A)
(fCod (Hom A)) . t1 is set
x is Element of Maps (Hom A)
cod x is Element of Hom A
t1 `1 is set
(t1 `1) `2 is set
[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))] `2 is set
dom t1 is Element of the carrier of (A)
the Source of (A) . t1 is Element of the carrier of (A)
(fDom (Hom A)) . t1 is set
dom x is Element of Hom A
(t1 `1) `1 is set
[(Hom ((dom F),(dom d))),(Hom ((dom F),(cod d)))] `1 is set
Hom (((A,(cod F)) . d1),((A,(dom F)) . d1)) is Element of K32( the carrier' of (A))
{ b₁ where b₁ is Element of the carrier' of (A) : ( dom b₁ = (A,(cod F)) . d1 & cod b₁ = (A,(dom F)) . d1 ) } is set
f (*) ta1 is Element of the carrier' of (A)
[(Hom ((cod F),(dom d))),(Hom ((dom F),d1))] is V1() set
{(Hom ((cod F),(dom d))),(Hom ((dom F),d1))} is non empty set
{{(Hom ((cod F),(dom d))),(Hom ((dom F),d1))},{(Hom ((cod F),(dom d)))}} is non empty set
[[(Hom ((cod F),(dom d))),(Hom ((dom F),d1))],((hom ((cod F),d)) * (hom (F,d1)))] is V1() set
{[(Hom ((cod F),(dom d))),(Hom ((dom F),d1))],((hom ((cod F),d)) * (hom (F,d1)))} is non empty set
{[(Hom ((cod F),(dom d))),(Hom ((dom F),d1))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),(dom d))),(Hom ((dom F),d1))],((hom ((cod F),d)) * (hom (F,d1)))},{[(Hom ((cod F),(dom d))),(Hom ((dom F),d1))]}} is non empty set
[(Hom ((cod F),t)),(Hom ((dom F),(cod d)))] is V1() set
{(Hom ((cod F),t)),(Hom ((dom F),(cod d)))} is non empty set
{{(Hom ((cod F),t)),(Hom ((dom F),(cod d)))},{(Hom ((cod F),t))}} is non empty set
[[(Hom ((cod F),t)),(Hom ((dom F),(cod d)))],((hom (F,t)) * (hom ((dom F),d)))] is V1() set
{[(Hom ((cod F),t)),(Hom ((dom F),(cod d)))],((hom (F,t)) * (hom ((dom F),d)))} is non empty set
{[(Hom ((cod F),t)),(Hom ((dom F),(cod d)))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),t)),(Hom ((dom F),(cod d)))],((hom (F,t)) * (hom ((dom F),d)))},{[(Hom ((cod F),t)),(Hom ((dom F),(cod d)))]}} is non empty set
t1 (*) t is Element of the carrier' of (A)
t is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod F)),(A,(dom F))
d1 is Element of the carrier of A
t . d1 is Morphism of (A,(cod F)) . d1,(A,(dom F)) . d1
(A,(cod F)) . d1 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . d1 is Element of the carrier of (A)
(A,(dom F)) . d1 is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . d1 is Element of the carrier of (A)
Hom ((cod F),d1) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = d1 ) } is set
Hom ((dom F),d1) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = d1 ) } is set
[(Hom ((cod F),d1)),(Hom ((dom F),d1))] is V1() set
{(Hom ((cod F),d1)),(Hom ((dom F),d1))} is non empty set
{(Hom ((cod F),d1))} is non empty set
{{(Hom ((cod F),d1)),(Hom ((dom F),d1))},{(Hom ((cod F),d1))}} is non empty set
id d1 is Morphism of d1,d1
hom (F,(id d1)) is Relation-like Hom ((cod F),(dom (id d1))) -defined Hom ((dom F),(cod (id d1))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),(dom (id d1)))),(Hom ((dom F),(cod (id d1))))))
dom (id d1) is Element of the carrier of A
the Source of A . (id d1) is Element of the carrier of A
Hom ((cod F),(dom (id d1))) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = dom (id d1) ) } is set
cod (id d1) is Element of the carrier of A
the Target of A . (id d1) is Element of the carrier of A
Hom ((dom F),(cod (id d1))) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = cod (id d1) ) } is set
K33((Hom ((cod F),(dom (id d1)))),(Hom ((dom F),(cod (id d1))))) is Relation-like set
K32(K33((Hom ((cod F),(dom (id d1)))),(Hom ((dom F),(cod (id d1)))))) is set
[[(Hom ((cod F),d1)),(Hom ((dom F),d1))],(hom (F,(id d1)))] is V1() set
{[(Hom ((cod F),d1)),(Hom ((dom F),d1))],(hom (F,(id d1)))} is non empty set
{[(Hom ((cod F),d1)),(Hom ((dom F),d1))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),d1)),(Hom ((dom F),d1))],(hom (F,(id d1)))},{[(Hom ((cod F),d1)),(Hom ((dom F),d1))]}} is non empty set
t . d1 is set
c is Element of the carrier of A
Hom ((cod F),c) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod F & cod b₁ = c ) } is set
Hom ((dom F),c) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom F & cod b₁ = c ) } is set
[(Hom ((cod F),c)),(Hom ((dom F),c))] is V1() set
{(Hom ((cod F),c)),(Hom ((dom F),c))} is non empty set
{(Hom ((cod F),c))} is non empty set
{{(Hom ((cod F),c)),(Hom ((dom F),c))},{(Hom ((cod F),c))}} is non empty set
hom (F,c) is Relation-like Hom ((cod F),c) -defined Hom ((dom F),c) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),c)),(Hom ((dom F),c))))
K33((Hom ((cod F),c)),(Hom ((dom F),c))) is Relation-like set
K32(K33((Hom ((cod F),c)),(Hom ((dom F),c)))) is set
[[(Hom ((cod F),c)),(Hom ((dom F),c))],(hom (F,c))] is V1() set
{[(Hom ((cod F),c)),(Hom ((dom F),c))],(hom (F,c))} is non empty set
{[(Hom ((cod F),c)),(Hom ((dom F),c))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),c)),(Hom ((dom F),c))],(hom (F,c))},{[(Hom ((cod F),c)),(Hom ((dom F),c))]}} is non empty set
(A,(cod F)) . c is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . c is Element of the carrier of (A)
(A,(dom F)) . c is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . c is Element of the carrier of (A)
Hom (((A,(cod F)) . c),((A,(dom F)) . c)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b₁ where b₁ is Element of the carrier' of (A) : ( dom b₁ = (A,(cod F)) . c & cod b₁ = (A,(dom F)) . c ) } is set
fDom (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
K33((Maps (Hom A)),(Hom A)) is Relation-like set
K32(K33((Maps (Hom A)),(Hom A))) is set
fCod (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
fComp (Hom A) is Relation-like K33((Maps (Hom A)),(Maps (Hom A))) -defined Maps (Hom A) -valued Function-like Element of K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))))
K33((Maps (Hom A)),(Maps (Hom A))) is Relation-like set
K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))) is Relation-like set
K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A)))) is set
CatStr(# (Hom A),(Maps (Hom A)),(fDom (Hom A)),(fCod (Hom A)),(fComp (Hom A)) #) is strict CatStr
c9 is Element of the carrier' of (A)
cod c9 is Element of the carrier of (A)
the Target of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
K33( the carrier' of (A), the carrier of (A)) is Relation-like set
K32(K33( the carrier' of (A), the carrier of (A))) is set
the Target of (A) . c9 is Element of the carrier of (A)
(fCod (Hom A)) . c9 is set
g is Element of Maps (Hom A)
cod g is Element of Hom A
c9 `1 is set
(c9 `1) `2 is set
[(Hom ((cod F),c)),(Hom ((dom F),c))] `2 is set
the carrier of (Ens (Hom A)) is non empty set
hom?- ((Hom A),(dom F)) is non empty Relation-like the carrier' of A -defined the carrier' of (Ens (Hom A)) -valued Function-like V17( the carrier' of A) quasi_total Functor of A, Ens (Hom A)
the carrier' of (Ens (Hom A)) is non empty set
Obj (hom?- ((Hom A),(dom F))) is non empty Relation-like the carrier of A -defined the carrier of (Ens (Hom A)) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Ens (Hom A))))
K33( the carrier of A, the carrier of (Ens (Hom A))) is Relation-like set
K32(K33( the carrier of A, the carrier of (Ens (Hom A)))) is set
(Obj (hom?- ((Hom A),(dom F)))) . c is Element of the carrier of (Ens (Hom A))
(hom?- ((Hom A),(dom F))) . c is Element of the carrier of (Ens (Hom A))
dom c9 is Element of the carrier of (A)
the Source of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
the Source of (A) . c9 is Element of the carrier of (A)
(fDom (Hom A)) . c9 is set
dom g is Element of Hom A
(c9 `1) `1 is set
[(Hom ((cod F),c)),(Hom ((dom F),c))] `1 is set
hom?- ((Hom A),(cod F)) is non empty Relation-like the carrier' of A -defined the carrier' of (Ens (Hom A)) -valued Function-like V17( the carrier' of A) quasi_total Functor of A, Ens (Hom A)
Obj (hom?- ((Hom A),(cod F))) is non empty Relation-like the carrier of A -defined the carrier of (Ens (Hom A)) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Ens (Hom A))))
(Obj (hom?- ((Hom A),(cod F)))) . c is Element of the carrier of (Ens (Hom A))
(hom?- ((Hom A),(cod F))) . c is Element of the carrier of (Ens (Hom A))
c is Element of the carrier of A
(A,(cod F)) . c is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . c is Element of the carrier of (A)
(A,(dom F)) . c is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . c is Element of the carrier of (A)
Hom (((A,(cod F)) . c),((A,(dom F)) . c)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,(cod F)) . c & cod b<sub>1</sub> = (A,(dom F)) . c ) } is set
c is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod F)),(A,(dom F))
c9 is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod F)),(A,(dom F))
g is Element of the carrier of A
c . g is Morphism of (A,(cod F)) . g,(A,(dom F)) . g
(A,(cod F)) . g is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F))) . g is Element of the carrier of (A)
(A,(dom F)) . g is Element of the carrier of (A)
Obj (A,(dom F)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F))) . g is Element of the carrier of (A)
Hom ((cod F),g) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod F & cod b<sub>1</sub> = g ) } is set
Hom ((dom F),g) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom F & cod b<sub>1</sub> = g ) } is set
[(Hom ((cod F),g)),(Hom ((dom F),g))] is V1() set
{(Hom ((cod F),g)),(Hom ((dom F),g))} is non empty set
{(Hom ((cod F),g))} is non empty set
{{(Hom ((cod F),g)),(Hom ((dom F),g))},{(Hom ((cod F),g))}} is non empty set
id g is Morphism of g,g
hom (F,(id g)) is Relation-like Hom ((cod F),(dom (id g))) -defined Hom ((dom F),(cod (id g))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F),(dom (id g)))),(Hom ((dom F),(cod (id g))))))
dom (id g) is Element of the carrier of A
the Source of A . (id g) is Element of the carrier of A
Hom ((cod F),(dom (id g))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod F & cod b<sub>1</sub> = dom (id g) ) } is set
cod (id g) is Element of the carrier of A
the Target of A . (id g) is Element of the carrier of A
Hom ((dom F),(cod (id g))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom F & cod b<sub>1</sub> = cod (id g) ) } is set
K33((Hom ((cod F),(dom (id g)))),(Hom ((dom F),(cod (id g))))) is Relation-like set
K32(K33((Hom ((cod F),(dom (id g)))),(Hom ((dom F),(cod (id g)))))) is set
[[(Hom ((cod F),g)),(Hom ((dom F),g))],(hom (F,(id g)))] is V1() set
{[(Hom ((cod F),g)),(Hom ((dom F),g))],(hom (F,(id g)))} is non empty set
{[(Hom ((cod F),g)),(Hom ((dom F),g))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F),g)),(Hom ((dom F),g))],(hom (F,(id g)))},{[(Hom ((cod F),g)),(Hom ((dom F),g))]}} is non empty set
c9 . g is Morphism of (A,(cod F)) . g,(A,(dom F)) . g
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
(A) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Hom A is non empty set
Ens (Hom A) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,(A)) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (A,(A))) is non empty set
F is Element of the carrier' of A
cod F is Element of the carrier of A
the carrier of A is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Target of A . F is Element of the carrier of A
(A,(cod F)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
the carrier' of (A) is non empty set
hom?- (cod F) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
Maps (Hom A) is non empty set
K33( the carrier' of A,(Maps (Hom A))) is Relation-like set
K32(K33( the carrier' of A,(Maps (Hom A)))) is set
dom F is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Source of A . F is Element of the carrier of A
(A,(dom F)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom F) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
[(A,(cod F)),(A,(dom F))] is V1() set
{(A,(cod F)),(A,(dom F))} is non empty functional set
{(A,(cod F))} is non empty functional set
{{(A,(cod F)),(A,(dom F))},{(A,(cod F))}} is non empty set
(A,F) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod F)),(A,(dom F))
[[(A,(cod F)),(A,(dom F))],(A,F)] is V1() set
{[(A,(cod F)),(A,(dom F))],(A,F)} is non empty set
{[(A,(cod F)),(A,(dom F))]} is non empty Relation-like Function-like set
{{[(A,(cod F)),(A,(dom F))],(A,F)},{[(A,(cod F)),(A,(dom F))]}} is non empty set
NatTrans (A,(A)) is non empty NatTrans-DOMAIN of A,(A)
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
(A) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Hom A is non empty set
Ens (Hom A) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,(A)) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (A,(A))) is non empty set
F is Element of the carrier' of A
cod F is Element of the carrier of A
the carrier of A is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Target of A . F is Element of the carrier of A
(A,(cod F)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
the carrier' of (A) is non empty set
hom?- (cod F) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
Maps (Hom A) is non empty set
K33( the carrier' of A,(Maps (Hom A))) is Relation-like set
K32(K33( the carrier' of A,(Maps (Hom A)))) is set
dom F is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Source of A . F is Element of the carrier of A
(A,(dom F)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom F) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
[(A,(cod F)),(A,(dom F))] is V1() set
{(A,(cod F)),(A,(dom F))} is non empty functional set
{(A,(cod F))} is non empty functional set
{{(A,(cod F)),(A,(dom F))},{(A,(cod F))}} is non empty set
(A,F) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod F)),(A,(dom F))
[[(A,(cod F)),(A,(dom F))],(A,F)] is V1() set
{[(A,(cod F)),(A,(dom F))],(A,F)} is non empty set
{[(A,(cod F)),(A,(dom F))]} is non empty Relation-like Function-like set
{{[(A,(cod F)),(A,(dom F))],(A,F)},{[(A,(cod F)),(A,(dom F))]}} is non empty set
K33( the carrier' of A, the carrier' of (Functors (A,(A)))) is Relation-like set
K32(K33( the carrier' of A, the carrier' of (Functors (A,(A))))) is set
F is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (A,(A))) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier' of (Functors (A,(A)))))
c9 is Element of the carrier' of A
dom c9 is Element of the carrier of A
the carrier of A is non empty set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Source of A . c9 is Element of the carrier of A
c is Element of the carrier' of A
cod c is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Target of A . c is Element of the carrier of A
c9 (*) c is Element of the carrier' of A
F . (c9 (*) c) is Element of the carrier' of (Functors (A,(A)))
F . c9 is Element of the carrier' of (Functors (A,(A)))
F . c is Element of the carrier' of (Functors (A,(A)))
(F . c) (*) (F . c9) is Element of the carrier' of (Functors (A,(A)))
the carrier' of (A) is non empty set
cod c9 is Element of the carrier of A
the Target of A . c9 is Element of the carrier of A
(A,(cod c9)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod c9) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
Maps (Hom A) is non empty set
K33( the carrier' of A,(Maps (Hom A))) is Relation-like set
K32(K33( the carrier' of A,(Maps (Hom A)))) is set
(A,(dom c9)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom c9) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
(A,c9) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod c9)),(A,(dom c9))
dom c is Element of the carrier of A
the Source of A . c is Element of the carrier of A
(A,(dom c)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom c) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
(A,c) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod c)),(A,(dom c))
(A,(cod c)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod c) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
[(A,(cod c9)),(A,(dom c9))] is V1() set
{(A,(cod c9)),(A,(dom c9))} is non empty functional set
{(A,(cod c9))} is non empty functional set
{{(A,(cod c9)),(A,(dom c9))},{(A,(cod c9))}} is non empty set
g is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod c9)),(A,(dom c9))
[[(A,(cod c9)),(A,(dom c9))],g] is V1() set
{[(A,(cod c9)),(A,(dom c9))],g} is non empty set
{[(A,(cod c9)),(A,(dom c9))]} is non empty Relation-like Function-like set
{{[(A,(cod c9)),(A,(dom c9))],g},{[(A,(cod c9)),(A,(dom c9))]}} is non empty set
dom (c9 (*) c) is Element of the carrier of A
the Source of A . (c9 (*) c) is Element of the carrier of A
cod (c9 (*) c) is Element of the carrier of A
the Target of A . (c9 (*) c) is Element of the carrier of A
(A,(cod (c9 (*) c))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod (c9 (*) c)) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
(A,(dom (c9 (*) c))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom (c9 (*) c)) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
F1 is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(dom c9)),(A,(dom c))
F1 `*` g is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod c9)),(A,(dom c))
(A,(c9 (*) c)) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod (c9 (*) c))),(A,(dom (c9 (*) c)))
F2 is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod (c9 (*) c))),(A,(dom (c9 (*) c)))
d is Element of the carrier of A
(A,(c9 (*) c)) . d is Morphism of (A,(cod (c9 (*) c))) . d,(A,(dom (c9 (*) c))) . d
(A,(cod (c9 (*) c))) . d is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod (c9 (*) c))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod (c9 (*) c)))) . d is Element of the carrier of (A)
(A,(dom (c9 (*) c))) . d is Element of the carrier of (A)
Obj (A,(dom (c9 (*) c))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom (c9 (*) c)))) . d is Element of the carrier of (A)
F2 . d is Morphism of (A,(cod (c9 (*) c))) . d,(A,(dom (c9 (*) c))) . d
F1 . d is Morphism of (A,(dom c9)) . d,(A,(dom c)) . d
(A,(dom c9)) . d is Element of the carrier of (A)
Obj (A,(dom c9)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom c9))) . d is Element of the carrier of (A)
(A,(dom c)) . d is Element of the carrier of (A)
Obj (A,(dom c)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom c))) . d is Element of the carrier of (A)
g . d is Morphism of (A,(cod c9)) . d,(A,(dom c9)) . d
(A,(cod c9)) . d is Element of the carrier of (A)
Obj (A,(cod c9)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(cod c9))) . d is Element of the carrier of (A)
t1 is Element of the carrier' of (A)
Hom ((cod c9),d) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod c9 & cod b<sub>1</sub> = d ) } is set
Hom ((dom c9),d) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom c9 & cod b<sub>1</sub> = d ) } is set
[(Hom ((cod c9),d)),(Hom ((dom c9),d))] is V1() set
{(Hom ((cod c9),d)),(Hom ((dom c9),d))} is non empty set
{(Hom ((cod c9),d))} is non empty set
{{(Hom ((cod c9),d)),(Hom ((dom c9),d))},{(Hom ((cod c9),d))}} is non empty set
id d is Morphism of d,d
hom (c9,(id d)) is Relation-like Hom ((cod c9),(dom (id d))) -defined Hom ((dom c9),(cod (id d))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod c9),(dom (id d)))),(Hom ((dom c9),(cod (id d))))))
dom (id d) is Element of the carrier of A
the Source of A . (id d) is Element of the carrier of A
Hom ((cod c9),(dom (id d))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod c9 & cod b<sub>1</sub> = dom (id d) ) } is set
cod (id d) is Element of the carrier of A
the Target of A . (id d) is Element of the carrier of A
Hom ((dom c9),(cod (id d))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom c9 & cod b<sub>1</sub> = cod (id d) ) } is set
K33((Hom ((cod c9),(dom (id d)))),(Hom ((dom c9),(cod (id d))))) is Relation-like set
K32(K33((Hom ((cod c9),(dom (id d)))),(Hom ((dom c9),(cod (id d)))))) is set
[[(Hom ((cod c9),d)),(Hom ((dom c9),d))],(hom (c9,(id d)))] is V1() set
{[(Hom ((cod c9),d)),(Hom ((dom c9),d))],(hom (c9,(id d)))} is non empty set
{[(Hom ((cod c9),d)),(Hom ((dom c9),d))]} is non empty Relation-like Function-like set
{{[(Hom ((cod c9),d)),(Hom ((dom c9),d))],(hom (c9,(id d)))},{[(Hom ((cod c9),d)),(Hom ((dom c9),d))]}} is non empty set
f is Element of the carrier of A
Hom ((cod c9),f) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod c9 & cod b<sub>1</sub> = f ) } is set
Hom ((dom c9),f) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom c9 & cod b<sub>1</sub> = f ) } is set
[(Hom ((cod c9),f)),(Hom ((dom c9),f))] is V1() set
{(Hom ((cod c9),f)),(Hom ((dom c9),f))} is non empty set
{(Hom ((cod c9),f))} is non empty set
{{(Hom ((cod c9),f)),(Hom ((dom c9),f))},{(Hom ((cod c9),f))}} is non empty set
hom (c9,f) is Relation-like Hom ((cod c9),f) -defined Hom ((dom c9),f) -valued Function-like quasi_total Element of K32(K33((Hom ((cod c9),f)),(Hom ((dom c9),f))))
K33((Hom ((cod c9),f)),(Hom ((dom c9),f))) is Relation-like set
K32(K33((Hom ((cod c9),f)),(Hom ((dom c9),f)))) is set
[[(Hom ((cod c9),f)),(Hom ((dom c9),f))],(hom (c9,f))] is V1() set
{[(Hom ((cod c9),f)),(Hom ((dom c9),f))],(hom (c9,f))} is non empty set
{[(Hom ((cod c9),f)),(Hom ((dom c9),f))]} is non empty Relation-like Function-like set
{{[(Hom ((cod c9),f)),(Hom ((dom c9),f))],(hom (c9,f))},{[(Hom ((cod c9),f)),(Hom ((dom c9),f))]}} is non empty set
(A,(cod c9)) . f is Element of the carrier of (A)
(Obj (A,(cod c9))) . f is Element of the carrier of (A)
(A,(dom c9)) . f is Element of the carrier of (A)
(Obj (A,(dom c9))) . f is Element of the carrier of (A)
Hom (((A,(cod c9)) . f),((A,(dom c9)) . f)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,(cod c9)) . f & cod b<sub>1</sub> = (A,(dom c9)) . f ) } is set
fDom (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
K33((Maps (Hom A)),(Hom A)) is Relation-like set
K32(K33((Maps (Hom A)),(Hom A))) is set
fCod (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
fComp (Hom A) is Relation-like K33((Maps (Hom A)),(Maps (Hom A))) -defined Maps (Hom A) -valued Function-like Element of K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))))
K33((Maps (Hom A)),(Maps (Hom A))) is Relation-like set
K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))) is Relation-like set
K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A)))) is set
CatStr(# (Hom A),(Maps (Hom A)),(fDom (Hom A)),(fCod (Hom A)),(fComp (Hom A)) #) is strict CatStr
a is Element of the carrier' of (A)
cod a is Element of the carrier of (A)
the Target of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
K33( the carrier' of (A), the carrier of (A)) is Relation-like set
K32(K33( the carrier' of (A), the carrier of (A))) is set
the Target of (A) . a is Element of the carrier of (A)
(fCod (Hom A)) . a is set
ta1 is Element of Maps (Hom A)
cod ta1 is Element of Hom A
a `1 is set
(a `1) `2 is set
[(Hom ((cod c9),f)),(Hom ((dom c9),f))] `2 is set
the carrier of (Ens (Hom A)) is non empty set
hom?- ((Hom A),(dom c9)) is non empty Relation-like the carrier' of A -defined the carrier' of (Ens (Hom A)) -valued Function-like V17( the carrier' of A) quasi_total Functor of A, Ens (Hom A)
the carrier' of (Ens (Hom A)) is non empty set
Obj (hom?- ((Hom A),(dom c9))) is non empty Relation-like the carrier of A -defined the carrier of (Ens (Hom A)) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Ens (Hom A))))
K33( the carrier of A, the carrier of (Ens (Hom A))) is Relation-like set
K32(K33( the carrier of A, the carrier of (Ens (Hom A)))) is set
(Obj (hom?- ((Hom A),(dom c9)))) . f is Element of the carrier of (Ens (Hom A))
(hom?- ((Hom A),(dom c9))) . f is Element of the carrier of (Ens (Hom A))
dom a is Element of the carrier of (A)
the Source of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
the Source of (A) . a is Element of the carrier of (A)
(fDom (Hom A)) . a is set
dom ta1 is Element of Hom A
(a `1) `1 is set
[(Hom ((cod c9),f)),(Hom ((dom c9),f))] `1 is set
hom?- ((Hom A),(cod c9)) is non empty Relation-like the carrier' of A -defined the carrier' of (Ens (Hom A)) -valued Function-like V17( the carrier' of A) quasi_total Functor of A, Ens (Hom A)
Obj (hom?- ((Hom A),(cod c9))) is non empty Relation-like the carrier of A -defined the carrier of (Ens (Hom A)) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Ens (Hom A))))
(Obj (hom?- ((Hom A),(cod c9)))) . f is Element of the carrier of (Ens (Hom A))
(hom?- ((Hom A),(cod c9))) . f is Element of the carrier of (Ens (Hom A))
Hom (((A,(cod c9)) . d),((A,(dom c9)) . d)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b₁ where b₁ is Element of the carrier' of (A) : ( dom b₁ = (A,(cod c9)) . d & cod b₁ = (A,(dom c9)) . d ) } is set
f is Element of the carrier of A
Hom ((cod c),f) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod c & cod b₁ = f ) } is set
Hom ((dom c),f) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom c & cod b₁ = f ) } is set
[(Hom ((cod c),f)),(Hom ((dom c),f))] is V1() set
{(Hom ((cod c),f)),(Hom ((dom c),f))} is non empty set
{(Hom ((cod c),f))} is non empty set
{{(Hom ((cod c),f)),(Hom ((dom c),f))},{(Hom ((cod c),f))}} is non empty set
hom (c,f) is Relation-like Hom ((cod c),f) -defined Hom ((dom c),f) -valued Function-like quasi_total Element of K32(K33((Hom ((cod c),f)),(Hom ((dom c),f))))
K33((Hom ((cod c),f)),(Hom ((dom c),f))) is Relation-like set
K32(K33((Hom ((cod c),f)),(Hom ((dom c),f)))) is set
[[(Hom ((cod c),f)),(Hom ((dom c),f))],(hom (c,f))] is V1() set
{[(Hom ((cod c),f)),(Hom ((dom c),f))],(hom (c,f))} is non empty set
{[(Hom ((cod c),f)),(Hom ((dom c),f))]} is non empty Relation-like Function-like set
{{[(Hom ((cod c),f)),(Hom ((dom c),f))],(hom (c,f))},{[(Hom ((cod c),f)),(Hom ((dom c),f))]}} is non empty set
(A,(cod c)) . f is Element of the carrier of (A)
Obj (A,(cod c)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(cod c))) . f is Element of the carrier of (A)
(A,(dom c)) . f is Element of the carrier of (A)
(Obj (A,(dom c))) . f is Element of the carrier of (A)
Hom (((A,(cod c)) . f),((A,(dom c)) . f)) is Element of K32( the carrier' of (A))
{ b₁ where b₁ is Element of the carrier' of (A) : ( dom b₁ = (A,(cod c)) . f & cod b₁ = (A,(dom c)) . f ) } is set
fDom (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
K33((Maps (Hom A)),(Hom A)) is Relation-like set
K32(K33((Maps (Hom A)),(Hom A))) is set
fCod (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
fComp (Hom A) is Relation-like K33((Maps (Hom A)),(Maps (Hom A))) -defined Maps (Hom A) -valued Function-like Element of K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))))
K33((Maps (Hom A)),(Maps (Hom A))) is Relation-like set
K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))) is Relation-like set
K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A)))) is set
CatStr(# (Hom A),(Maps (Hom A)),(fDom (Hom A)),(fCod (Hom A)),(fComp (Hom A)) #) is strict CatStr
a is Element of the carrier' of (A)
cod a is Element of the carrier of (A)
the Target of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
K33( the carrier' of (A), the carrier of (A)) is Relation-like set
K32(K33( the carrier' of (A), the carrier of (A))) is set
the Target of (A) . a is Element of the carrier of (A)
(fCod (Hom A)) . a is set
ta1 is Element of Maps (Hom A)
cod ta1 is Element of Hom A
a `1 is set
(a `1) `2 is set
[(Hom ((cod c),f)),(Hom ((dom c),f))] `2 is set
the carrier of (Ens (Hom A)) is non empty set
hom?- ((Hom A),(dom c)) is non empty Relation-like the carrier' of A -defined the carrier' of (Ens (Hom A)) -valued Function-like V17( the carrier' of A) quasi_total Functor of A, Ens (Hom A)
the carrier' of (Ens (Hom A)) is non empty set
Obj (hom?- ((Hom A),(dom c))) is non empty Relation-like the carrier of A -defined the carrier of (Ens (Hom A)) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Ens (Hom A))))
K33( the carrier of A, the carrier of (Ens (Hom A))) is Relation-like set
K32(K33( the carrier of A, the carrier of (Ens (Hom A)))) is set
(Obj (hom?- ((Hom A),(dom c)))) . f is Element of the carrier of (Ens (Hom A))
(hom?- ((Hom A),(dom c))) . f is Element of the carrier of (Ens (Hom A))
dom a is Element of the carrier of (A)
the Source of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
the Source of (A) . a is Element of the carrier of (A)
(fDom (Hom A)) . a is set
dom ta1 is Element of Hom A
(a `1) `1 is set
[(Hom ((cod c),f)),(Hom ((dom c),f))] `1 is set
hom?- ((Hom A),(cod c)) is non empty Relation-like the carrier' of A -defined the carrier' of (Ens (Hom A)) -valued Function-like V17( the carrier' of A) quasi_total Functor of A, Ens (Hom A)
Obj (hom?- ((Hom A),(cod c))) is non empty Relation-like the carrier of A -defined the carrier of (Ens (Hom A)) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Ens (Hom A))))
(Obj (hom?- ((Hom A),(cod c)))) . f is Element of the carrier of (Ens (Hom A))
(hom?- ((Hom A),(cod c))) . f is Element of the carrier of (Ens (Hom A))
(A,(cod c)) . d is Element of the carrier of (A)
Obj (A,(cod c)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(cod c))) . d is Element of the carrier of (A)
Hom (((A,(cod c)) . d),((A,(dom c)) . d)) is Element of K32( the carrier' of (A))
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,(cod c)) . d & cod b<sub>1</sub> = (A,(dom c)) . d ) } is set
Hom ((dom (c9 (*) c)),d) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (c9 (*) c) & cod b<sub>1</sub> = d ) } is set
[(Hom ((cod c9),d)),(Hom ((dom (c9 (*) c)),d))] is V1() set
{(Hom ((cod c9),d)),(Hom ((dom (c9 (*) c)),d))} is non empty set
{{(Hom ((cod c9),d)),(Hom ((dom (c9 (*) c)),d))},{(Hom ((cod c9),d))}} is non empty set
hom ((c9 (*) c),(id d)) is Relation-like Hom ((cod (c9 (*) c)),(dom (id d))) -defined Hom ((dom (c9 (*) c)),(cod (id d))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod (c9 (*) c)),(dom (id d)))),(Hom ((dom (c9 (*) c)),(cod (id d))))))
Hom ((cod (c9 (*) c)),(dom (id d))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (c9 (*) c) & cod b<sub>1</sub> = dom (id d) ) } is set
Hom ((dom (c9 (*) c)),(cod (id d))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (c9 (*) c) & cod b<sub>1</sub> = cod (id d) ) } is set
K33((Hom ((cod (c9 (*) c)),(dom (id d)))),(Hom ((dom (c9 (*) c)),(cod (id d))))) is Relation-like set
K32(K33((Hom ((cod (c9 (*) c)),(dom (id d)))),(Hom ((dom (c9 (*) c)),(cod (id d)))))) is set
[[(Hom ((cod c9),d)),(Hom ((dom (c9 (*) c)),d))],(hom ((c9 (*) c),(id d)))] is V1() set
{[(Hom ((cod c9),d)),(Hom ((dom (c9 (*) c)),d))],(hom ((c9 (*) c),(id d)))} is non empty set
{[(Hom ((cod c9),d)),(Hom ((dom (c9 (*) c)),d))]} is non empty Relation-like Function-like set
{{[(Hom ((cod c9),d)),(Hom ((dom (c9 (*) c)),d))],(hom ((c9 (*) c),(id d)))},{[(Hom ((cod c9),d)),(Hom ((dom (c9 (*) c)),d))]}} is non empty set
Hom ((dom c),d) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom c & cod b<sub>1</sub> = d ) } is set
[(Hom ((cod c9),d)),(Hom ((dom c),d))] is V1() set
{(Hom ((cod c9),d)),(Hom ((dom c),d))} is non empty set
{{(Hom ((cod c9),d)),(Hom ((dom c),d))},{(Hom ((cod c9),d))}} is non empty set
hom ((c9 (*) c),d) is Relation-like Hom ((cod (c9 (*) c)),d) -defined Hom ((dom (c9 (*) c)),d) -valued Function-like quasi_total Element of K32(K33((Hom ((cod (c9 (*) c)),d)),(Hom ((dom (c9 (*) c)),d))))
Hom ((cod (c9 (*) c)),d) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (c9 (*) c) & cod b<sub>1</sub> = d ) } is set
K33((Hom ((cod (c9 (*) c)),d)),(Hom ((dom (c9 (*) c)),d))) is Relation-like set
K32(K33((Hom ((cod (c9 (*) c)),d)),(Hom ((dom (c9 (*) c)),d)))) is set
[[(Hom ((cod c9),d)),(Hom ((dom c),d))],(hom ((c9 (*) c),d))] is V1() set
{[(Hom ((cod c9),d)),(Hom ((dom c),d))],(hom ((c9 (*) c),d))} is non empty set
{[(Hom ((cod c9),d)),(Hom ((dom c),d))]} is non empty Relation-like Function-like set
{{[(Hom ((cod c9),d)),(Hom ((dom c),d))],(hom ((c9 (*) c),d))},{[(Hom ((cod c9),d)),(Hom ((dom c),d))]}} is non empty set
Hom ((cod c),d) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod c & cod b<sub>1</sub> = d ) } is set
[(Hom ((cod c),d)),(Hom ((dom c),d))] is V1() set
{(Hom ((cod c),d)),(Hom ((dom c),d))} is non empty set
{(Hom ((cod c),d))} is non empty set
{{(Hom ((cod c),d)),(Hom ((dom c),d))},{(Hom ((cod c),d))}} is non empty set
hom (c,(id d)) is Relation-like Hom ((cod c),(dom (id d))) -defined Hom ((dom c),(cod (id d))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod c),(dom (id d)))),(Hom ((dom c),(cod (id d))))))
Hom ((cod c),(dom (id d))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod c & cod b<sub>1</sub> = dom (id d) ) } is set
Hom ((dom c),(cod (id d))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom c & cod b<sub>1</sub> = cod (id d) ) } is set
K33((Hom ((cod c),(dom (id d)))),(Hom ((dom c),(cod (id d))))) is Relation-like set
K32(K33((Hom ((cod c),(dom (id d)))),(Hom ((dom c),(cod (id d)))))) is set
[[(Hom ((cod c),d)),(Hom ((dom c),d))],(hom (c,(id d)))] is V1() set
{[(Hom ((cod c),d)),(Hom ((dom c),d))],(hom (c,(id d)))} is non empty set
{[(Hom ((cod c),d)),(Hom ((dom c),d))]} is non empty Relation-like Function-like set
{{[(Hom ((cod c),d)),(Hom ((dom c),d))],(hom (c,(id d)))},{[(Hom ((cod c),d)),(Hom ((dom c),d))]}} is non empty set
fDom (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
K33((Maps (Hom A)),(Hom A)) is Relation-like set
K32(K33((Maps (Hom A)),(Hom A))) is set
fCod (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
fComp (Hom A) is Relation-like K33((Maps (Hom A)),(Maps (Hom A))) -defined Maps (Hom A) -valued Function-like Element of K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))))
K33((Maps (Hom A)),(Maps (Hom A))) is Relation-like set
K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))) is Relation-like set
K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A)))) is set
CatStr(# (Hom A),(Maps (Hom A)),(fDom (Hom A)),(fCod (Hom A)),(fComp (Hom A)) #) is strict CatStr
t is Element of the carrier' of (A)
cod t1 is Element of the carrier of (A)
the Target of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
K33( the carrier' of (A), the carrier of (A)) is Relation-like set
K32(K33( the carrier' of (A), the carrier of (A))) is set
the Target of (A) . t1 is Element of the carrier of (A)
(fCod (Hom A)) . t1 is set
a is Element of Maps (Hom A)
cod a is Element of Hom A
t1 `1 is set
(t1 `1) `2 is set
[(Hom ((cod c9),d)),(Hom ((dom c9),d))] `2 is set
cod t is Element of the carrier of (A)
the Target of (A) . t is Element of the carrier of (A)
(fCod (Hom A)) . t is set
f is Element of Maps (Hom A)
cod f is Element of Hom A
t `1 is set
(t `1) `2 is set
[(Hom ((cod c),d)),(Hom ((dom c),d))] `2 is set
dom t is Element of the carrier of (A)
the Source of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
the Source of (A) . t is Element of the carrier of (A)
(fDom (Hom A)) . t is set
dom f is Element of Hom A
(t `1) `1 is set
[(Hom ((cod c),d)),(Hom ((dom c),d))] `1 is set
dom t1 is Element of the carrier of (A)
the Source of (A) . t1 is Element of the carrier of (A)
(fDom (Hom A)) . t1 is set
dom a is Element of Hom A
(t1 `1) `1 is set
[(Hom ((cod c9),d)),(Hom ((dom c9),d))] `1 is set
(F1 . d) * (g . d) is Morphism of (A,(cod c9)) . d,(A,(dom c)) . d
t (*) t1 is Element of the carrier' of (A)
(hom (c9,(id d))) * (hom (c,(id d))) is Relation-like Hom ((cod c9),(dom (id d))) -defined Hom ((dom c),(cod (id d))) -valued Function-like set
[[(Hom ((cod c9),d)),(Hom ((dom c),d))],((hom (c9,(id d))) * (hom (c,(id d))))] is V1() set
{[(Hom ((cod c9),d)),(Hom ((dom c),d))],((hom (c9,(id d))) * (hom (c,(id d))))} is non empty set
{{[(Hom ((cod c9),d)),(Hom ((dom c),d))],((hom (c9,(id d))) * (hom (c,(id d))))},{[(Hom ((cod c9),d)),(Hom ((dom c),d))]}} is non empty set
hom (c,d) is Relation-like Hom ((cod c),d) -defined Hom ((dom c),d) -valued Function-like quasi_total Element of K32(K33((Hom ((cod c),d)),(Hom ((dom c),d))))
K33((Hom ((cod c),d)),(Hom ((dom c),d))) is Relation-like set
K32(K33((Hom ((cod c),d)),(Hom ((dom c),d)))) is set
(hom (c9,(id d))) * (hom (c,d)) is Relation-like Hom ((cod c9),(dom (id d))) -defined Hom ((dom c),d) -valued Function-like set
[[(Hom ((cod c9),d)),(Hom ((dom c),d))],((hom (c9,(id d))) * (hom (c,d)))] is V1() set
{[(Hom ((cod c9),d)),(Hom ((dom c),d))],((hom (c9,(id d))) * (hom (c,d)))} is non empty set
{{[(Hom ((cod c9),d)),(Hom ((dom c),d))],((hom (c9,(id d))) * (hom (c,d)))},{[(Hom ((cod c9),d)),(Hom ((dom c),d))]}} is non empty set
hom (c9,d) is Relation-like Hom ((cod c9),d) -defined Hom ((dom c9),d) -valued Function-like quasi_total Element of K32(K33((Hom ((cod c9),d)),(Hom ((dom c9),d))))
K33((Hom ((cod c9),d)),(Hom ((dom c9),d))) is Relation-like set
K32(K33((Hom ((cod c9),d)),(Hom ((dom c9),d)))) is set
(hom (c9,d)) * (hom (c,d)) is Relation-like Hom ((cod c9),d) -defined Hom ((dom c),d) -valued Function-like set
[[(Hom ((cod c9),d)),(Hom ((dom c),d))],((hom (c9,d)) * (hom (c,d)))] is V1() set
{[(Hom ((cod c9),d)),(Hom ((dom c),d))],((hom (c9,d)) * (hom (c,d)))} is non empty set
{{[(Hom ((cod c9),d)),(Hom ((dom c),d))],((hom (c9,d)) * (hom (c,d)))},{[(Hom ((cod c9),d)),(Hom ((dom c),d))]}} is non empty set
[(A,(dom c9)),(A,(dom c))] is V1() set
{(A,(dom c9)),(A,(dom c))} is non empty functional set
{(A,(dom c9))} is non empty functional set
{{(A,(dom c9)),(A,(dom c))},{(A,(dom c9))}} is non empty set
[[(A,(dom c9)),(A,(dom c))],F1] is V1() set
{[(A,(dom c9)),(A,(dom c))],F1} is non empty set
{[(A,(dom c9)),(A,(dom c))]} is non empty Relation-like Function-like set
{{[(A,(dom c9)),(A,(dom c))],F1},{[(A,(dom c9)),(A,(dom c))]}} is non empty set
[(F . c),(F . c9)] is V1() Element of the carrier' of K210((Functors (A,(A))),(Functors (A,(A))))
K210((Functors (A,(A))),(Functors (A,(A)))) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of K210((Functors (A,(A))),(Functors (A,(A)))) is non empty set
{(F . c),(F . c9)} is non empty set
{(F . c)} is non empty set
{{(F . c),(F . c9)},{(F . c)}} is non empty set
the Comp of (Functors (A,(A))) is Relation-like K33( the carrier' of (Functors (A,(A))), the carrier' of (Functors (A,(A)))) -defined the carrier' of (Functors (A,(A))) -valued Function-like Element of K32(K33(K33( the carrier' of (Functors (A,(A))), the carrier' of (Functors (A,(A)))), the carrier' of (Functors (A,(A)))))
K33( the carrier' of (Functors (A,(A))), the carrier' of (Functors (A,(A)))) is Relation-like set
K33(K33( the carrier' of (Functors (A,(A))), the carrier' of (Functors (A,(A)))), the carrier' of (Functors (A,(A)))) is Relation-like set
K32(K33(K33( the carrier' of (Functors (A,(A))), the carrier' of (Functors (A,(A)))), the carrier' of (Functors (A,(A))))) is set
proj1 the Comp of (Functors (A,(A))) is Relation-like set
the Comp of (Functors (A,(A))) . ((F . c),(F . c9)) is set
[(F . c),(F . c9)] is V1() set
the Comp of (Functors (A,(A))) . [(F . c),(F . c9)] is set
t is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
d1 is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
d is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
[t,d1] is V1() set
{t,d1} is non empty functional set
{t} is non empty functional set
{{t,d1},{t}} is non empty set
t is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of t,d1
[[t,d1],t] is V1() set
{[t,d1],t} is non empty set
{[t,d1]} is non empty Relation-like Function-like set
{{[t,d1],t},{[t,d1]}} is non empty set
[d1,d] is V1() set
{d1,d} is non empty functional set
{d1} is non empty functional set
{{d1,d},{d1}} is non empty set
t1 is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of d1,d
[[d1,d],t1] is V1() set
{[d1,d],t1} is non empty set
{[d1,d]} is non empty Relation-like Function-like set
{{[d1,d],t1},{[d1,d]}} is non empty set
[t,d] is V1() set
{t,d} is non empty functional set
{{t,d},{t}} is non empty set
t1 `*` t is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of t,d
[[t,d],(t1 `*` t)] is V1() set
{[t,d],(t1 `*` t)} is non empty set
{[t,d]} is non empty Relation-like Function-like set
{{[t,d],(t1 `*` t)},{[t,d]}} is non empty set
[(A,(cod c9)),(A,(dom c))] is V1() set
{(A,(cod c9)),(A,(dom c))} is non empty functional set
{{(A,(cod c9)),(A,(dom c))},{(A,(cod c9))}} is non empty set
[[(A,(cod c9)),(A,(dom c))],(F1 `*` g)] is V1() set
{[(A,(cod c9)),(A,(dom c))],(F1 `*` g)} is non empty set
{[(A,(cod c9)),(A,(dom c))]} is non empty Relation-like Function-like set
{{[(A,(cod c9)),(A,(dom c))],(F1 `*` g)},{[(A,(cod c9)),(A,(dom c))]}} is non empty set
c is Element of the carrier' of A
dom c is Element of the carrier of A
the carrier of A is non empty set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Source of A . c is Element of the carrier of A
id (dom c) is Morphism of dom c, dom c
F . (id (dom c)) is Element of the carrier' of (Functors (A,(A)))
F . c is Element of the carrier' of (Functors (A,(A)))
cod (F . c) is Element of the carrier of (Functors (A,(A)))
the carrier of (Functors (A,(A))) is non empty set
the Target of (Functors (A,(A))) is non empty Relation-like the carrier' of (Functors (A,(A))) -defined the carrier of (Functors (A,(A))) -valued Function-like V17( the carrier' of (Functors (A,(A)))) quasi_total Element of K32(K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A)))))
K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A)))) is Relation-like set
K32(K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A))))) is set
the Target of (Functors (A,(A))) . (F . c) is Element of the carrier of (Functors (A,(A)))
id (cod (F . c)) is Morphism of cod (F . c), cod (F . c)
cod c is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Target of A . c is Element of the carrier of A
id (cod c) is Morphism of cod c, cod c
F . (id (cod c)) is Element of the carrier' of (Functors (A,(A)))
dom (F . c) is Element of the carrier of (Functors (A,(A)))
the Source of (Functors (A,(A))) is non empty Relation-like the carrier' of (Functors (A,(A))) -defined the carrier of (Functors (A,(A))) -valued Function-like V17( the carrier' of (Functors (A,(A)))) quasi_total Element of K32(K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A)))))
the Source of (Functors (A,(A))) . (F . c) is Element of the carrier of (Functors (A,(A)))
id (dom (F . c)) is Morphism of dom (F . c), dom (F . c)
(A,(id (dom c))) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod (id (dom c)))),(A,(dom (id (dom c))))
the carrier' of (A) is non empty set
cod (id (dom c)) is Element of the carrier of A
the Target of A . (id (dom c)) is Element of the carrier of A
(A,(cod (id (dom c)))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod (id (dom c))) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
Maps (Hom A) is non empty set
K33( the carrier' of A,(Maps (Hom A))) is Relation-like set
K32(K33( the carrier' of A,(Maps (Hom A)))) is set
dom (id (dom c)) is Element of the carrier of A
the Source of A . (id (dom c)) is Element of the carrier of A
(A,(dom (id (dom c)))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom (id (dom c))) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
proj1 (A,(id (dom c))) is non empty set
(A,(dom c)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom c) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
id (A,(dom c)) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(dom c)),(A,(dom c))
proj1 (id (A,(dom c))) is non empty set
[(A,(cod (id (dom c)))),(A,(dom (id (dom c))))] is V1() set
{(A,(cod (id (dom c)))),(A,(dom (id (dom c))))} is non empty functional set
{(A,(cod (id (dom c))))} is non empty functional set
{{(A,(cod (id (dom c)))),(A,(dom (id (dom c))))},{(A,(cod (id (dom c))))}} is non empty set
[[(A,(cod (id (dom c)))),(A,(dom (id (dom c))))],(A,(id (dom c)))] is V1() set
{[(A,(cod (id (dom c)))),(A,(dom (id (dom c))))],(A,(id (dom c)))} is non empty set
{[(A,(cod (id (dom c)))),(A,(dom (id (dom c))))]} is non empty Relation-like Function-like set
{{[(A,(cod (id (dom c)))),(A,(dom (id (dom c))))],(A,(id (dom c)))},{[(A,(cod (id (dom c)))),(A,(dom (id (dom c))))]}} is non empty set
[(A,(dom c)),(A,(dom (id (dom c))))] is V1() set
{(A,(dom c)),(A,(dom (id (dom c))))} is non empty functional set
{(A,(dom c))} is non empty functional set
{{(A,(dom c)),(A,(dom (id (dom c))))},{(A,(dom c))}} is non empty set
[[(A,(dom c)),(A,(dom (id (dom c))))],(A,(id (dom c)))] is V1() set
{[(A,(dom c)),(A,(dom (id (dom c))))],(A,(id (dom c)))} is non empty set
{[(A,(dom c)),(A,(dom (id (dom c))))]} is non empty Relation-like Function-like set
{{[(A,(dom c)),(A,(dom (id (dom c))))],(A,(id (dom c)))},{[(A,(dom c)),(A,(dom (id (dom c))))]}} is non empty set
[(A,(dom c)),(A,(dom c))] is V1() set
{(A,(dom c)),(A,(dom c))} is non empty functional set
{{(A,(dom c)),(A,(dom c))},{(A,(dom c))}} is non empty set
[[(A,(dom c)),(A,(dom c))],(A,(id (dom c)))] is V1() set
{[(A,(dom c)),(A,(dom c))],(A,(id (dom c)))} is non empty set
{[(A,(dom c)),(A,(dom c))]} is non empty Relation-like Function-like set
{{[(A,(dom c)),(A,(dom c))],(A,(id (dom c)))},{[(A,(dom c)),(A,(dom c))]}} is non empty set
(A,(cod c)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod c) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
[(A,(cod c)),(A,(dom c))] is V1() set
{(A,(cod c)),(A,(dom c))} is non empty functional set
{(A,(cod c))} is non empty functional set
{{(A,(cod c)),(A,(dom c))},{(A,(cod c))}} is non empty set
(A,c) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod c)),(A,(dom c))
[[(A,(cod c)),(A,(dom c))],(A,c)] is V1() set
{[(A,(cod c)),(A,(dom c))],(A,c)} is non empty set
{[(A,(cod c)),(A,(dom c))]} is non empty Relation-like Function-like set
{{[(A,(cod c)),(A,(dom c))],(A,c)},{[(A,(cod c)),(A,(dom c))]}} is non empty set
[[(A,(dom c)),(A,(dom c))],(id (A,(dom c)))] is V1() set
{[(A,(dom c)),(A,(dom c))],(id (A,(dom c)))} is non empty set
{{[(A,(dom c)),(A,(dom c))],(id (A,(dom c)))},{[(A,(dom c)),(A,(dom c))]}} is non empty set
F1 is set
(A,(id (dom c))) . F1 is set
(id (A,(dom c))) . F1 is set
F2 is Element of the carrier of A
id F2 is Morphism of F2,F2
Hom (F2,F2) is non empty Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = F2 & cod b<sub>1</sub> = F2 ) } is set
(A,(id (dom c))) . F2 is Morphism of (A,(cod (id (dom c)))) . F2,(A,(dom (id (dom c)))) . F2
(A,(cod (id (dom c)))) . F2 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod (id (dom c)))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod (id (dom c))))) . F2 is Element of the carrier of (A)
(A,(dom (id (dom c)))) . F2 is Element of the carrier of (A)
Obj (A,(dom (id (dom c)))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom (id (dom c))))) . F2 is Element of the carrier of (A)
Hom ((cod (id (dom c))),F2) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id (dom c)) & cod b<sub>1</sub> = F2 ) } is set
Hom ((dom (id (dom c))),F2) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id (dom c)) & cod b<sub>1</sub> = F2 ) } is set
[(Hom ((cod (id (dom c))),F2)),(Hom ((dom (id (dom c))),F2))] is V1() set
{(Hom ((cod (id (dom c))),F2)),(Hom ((dom (id (dom c))),F2))} is non empty set
{(Hom ((cod (id (dom c))),F2))} is non empty set
{{(Hom ((cod (id (dom c))),F2)),(Hom ((dom (id (dom c))),F2))},{(Hom ((cod (id (dom c))),F2))}} is non empty set
hom ((id (dom c)),(id F2)) is Relation-like Hom ((cod (id (dom c))),(dom (id F2))) -defined Hom ((dom (id (dom c))),(cod (id F2))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod (id (dom c))),(dom (id F2)))),(Hom ((dom (id (dom c))),(cod (id F2))))))
dom (id F2) is Element of the carrier of A
the Source of A . (id F2) is Element of the carrier of A
Hom ((cod (id (dom c))),(dom (id F2))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id (dom c)) & cod b<sub>1</sub> = dom (id F2) ) } is set
cod (id F2) is Element of the carrier of A
the Target of A . (id F2) is Element of the carrier of A
Hom ((dom (id (dom c))),(cod (id F2))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id (dom c)) & cod b<sub>1</sub> = cod (id F2) ) } is set
K33((Hom ((cod (id (dom c))),(dom (id F2)))),(Hom ((dom (id (dom c))),(cod (id F2))))) is Relation-like set
K32(K33((Hom ((cod (id (dom c))),(dom (id F2)))),(Hom ((dom (id (dom c))),(cod (id F2)))))) is set
[[(Hom ((cod (id (dom c))),F2)),(Hom ((dom (id (dom c))),F2))],(hom ((id (dom c)),(id F2)))] is V1() set
{[(Hom ((cod (id (dom c))),F2)),(Hom ((dom (id (dom c))),F2))],(hom ((id (dom c)),(id F2)))} is non empty set
{[(Hom ((cod (id (dom c))),F2)),(Hom ((dom (id (dom c))),F2))]} is non empty Relation-like Function-like set
{{[(Hom ((cod (id (dom c))),F2)),(Hom ((dom (id (dom c))),F2))],(hom ((id (dom c)),(id F2)))},{[(Hom ((cod (id (dom c))),F2)),(Hom ((dom (id (dom c))),F2))]}} is non empty set
Hom ((dom c),F2) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom c & cod b<sub>1</sub> = F2 ) } is set
[(Hom ((dom c),F2)),(Hom ((dom (id (dom c))),F2))] is V1() set
{(Hom ((dom c),F2)),(Hom ((dom (id (dom c))),F2))} is non empty set
{(Hom ((dom c),F2))} is non empty set
{{(Hom ((dom c),F2)),(Hom ((dom (id (dom c))),F2))},{(Hom ((dom c),F2))}} is non empty set
[[(Hom ((dom c),F2)),(Hom ((dom (id (dom c))),F2))],(hom ((id (dom c)),(id F2)))] is V1() set
{[(Hom ((dom c),F2)),(Hom ((dom (id (dom c))),F2))],(hom ((id (dom c)),(id F2)))} is non empty set
{[(Hom ((dom c),F2)),(Hom ((dom (id (dom c))),F2))]} is non empty Relation-like Function-like set
{{[(Hom ((dom c),F2)),(Hom ((dom (id (dom c))),F2))],(hom ((id (dom c)),(id F2)))},{[(Hom ((dom c),F2)),(Hom ((dom (id (dom c))),F2))]}} is non empty set
[(Hom ((dom c),F2)),(Hom ((dom c),F2))] is V1() set
{(Hom ((dom c),F2)),(Hom ((dom c),F2))} is non empty set
{{(Hom ((dom c),F2)),(Hom ((dom c),F2))},{(Hom ((dom c),F2))}} is non empty set
[[(Hom ((dom c),F2)),(Hom ((dom c),F2))],(hom ((id (dom c)),(id F2)))] is V1() set
{[(Hom ((dom c),F2)),(Hom ((dom c),F2))],(hom ((id (dom c)),(id F2)))} is non empty set
{[(Hom ((dom c),F2)),(Hom ((dom c),F2))]} is non empty Relation-like Function-like set
{{[(Hom ((dom c),F2)),(Hom ((dom c),F2))],(hom ((id (dom c)),(id F2)))},{[(Hom ((dom c),F2)),(Hom ((dom c),F2))]}} is non empty set
hom ((dom c),(id F2)) is Relation-like Hom ((dom c),(dom (id F2))) -defined Hom ((dom c),(cod (id F2))) -valued Function-like quasi_total Element of K32(K33((Hom ((dom c),(dom (id F2)))),(Hom ((dom c),(cod (id F2))))))
Hom ((dom c),(dom (id F2))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom c & cod b<sub>1</sub> = dom (id F2) ) } is set
Hom ((dom c),(cod (id F2))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom c & cod b<sub>1</sub> = cod (id F2) ) } is set
K33((Hom ((dom c),(dom (id F2)))),(Hom ((dom c),(cod (id F2))))) is Relation-like set
K32(K33((Hom ((dom c),(dom (id F2)))),(Hom ((dom c),(cod (id F2)))))) is set
[[(Hom ((dom c),F2)),(Hom ((dom c),F2))],(hom ((dom c),(id F2)))] is V1() set
{[(Hom ((dom c),F2)),(Hom ((dom c),F2))],(hom ((dom c),(id F2)))} is non empty set
{{[(Hom ((dom c),F2)),(Hom ((dom c),F2))],(hom ((dom c),(id F2)))},{[(Hom ((dom c),F2)),(Hom ((dom c),F2))]}} is non empty set
[(Hom ((dom c),F2)),(Hom ((dom c),(cod (id F2))))] is V1() set
{(Hom ((dom c),F2)),(Hom ((dom c),(cod (id F2))))} is non empty set
{{(Hom ((dom c),F2)),(Hom ((dom c),(cod (id F2))))},{(Hom ((dom c),F2))}} is non empty set
[[(Hom ((dom c),F2)),(Hom ((dom c),(cod (id F2))))],(hom ((dom c),(id F2)))] is V1() set
{[(Hom ((dom c),F2)),(Hom ((dom c),(cod (id F2))))],(hom ((dom c),(id F2)))} is non empty set
{[(Hom ((dom c),F2)),(Hom ((dom c),(cod (id F2))))]} is non empty Relation-like Function-like set
{{[(Hom ((dom c),F2)),(Hom ((dom c),(cod (id F2))))],(hom ((dom c),(id F2)))},{[(Hom ((dom c),F2)),(Hom ((dom c),(cod (id F2))))]}} is non empty set
[(Hom ((dom c),(dom (id F2)))),(Hom ((dom c),(cod (id F2))))] is V1() set
{(Hom ((dom c),(dom (id F2)))),(Hom ((dom c),(cod (id F2))))} is non empty set
{(Hom ((dom c),(dom (id F2))))} is non empty set
{{(Hom ((dom c),(dom (id F2)))),(Hom ((dom c),(cod (id F2))))},{(Hom ((dom c),(dom (id F2))))}} is non empty set
[[(Hom ((dom c),(dom (id F2)))),(Hom ((dom c),(cod (id F2))))],(hom ((dom c),(id F2)))] is V1() set
{[(Hom ((dom c),(dom (id F2)))),(Hom ((dom c),(cod (id F2))))],(hom ((dom c),(id F2)))} is non empty set
{[(Hom ((dom c),(dom (id F2)))),(Hom ((dom c),(cod (id F2))))]} is non empty Relation-like Function-like set
{{[(Hom ((dom c),(dom (id F2)))),(Hom ((dom c),(cod (id F2))))],(hom ((dom c),(id F2)))},{[(Hom ((dom c),(dom (id F2)))),(Hom ((dom c),(cod (id F2))))]}} is non empty set
(A,(dom c)) . (id F2) is set
t is Morphism of F2,F2
(A,(dom c)) /. t is Morphism of (A,(dom c)) . F2,(A,(dom c)) . F2
(A,(dom c)) . F2 is Element of the carrier of (A)
Obj (A,(dom c)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom c))) . F2 is Element of the carrier of (A)
id ((A,(dom c)) . F2) is Morphism of (A,(dom c)) . F2,(A,(dom c)) . F2
(id (A,(dom c))) . F2 is Morphism of (A,(dom c)) . F2,(A,(dom c)) . F2
(id (A,(dom c))) . F2 is set
(A,(id (cod c))) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod (id (cod c)))),(A,(dom (id (cod c))))
cod (id (cod c)) is Element of the carrier of A
the Target of A . (id (cod c)) is Element of the carrier of A
(A,(cod (id (cod c)))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod (id (cod c))) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
dom (id (cod c)) is Element of the carrier of A
the Source of A . (id (cod c)) is Element of the carrier of A
(A,(dom (id (cod c)))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom (id (cod c))) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
proj1 (A,(id (cod c))) is non empty set
id (A,(cod c)) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod c)),(A,(cod c))
F2 is set
(A,(id (cod c))) . F2 is set
(id (A,(cod c))) . F2 is set
t is Element of the carrier of A
Hom (t,t) is non empty Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = t & cod b<sub>1</sub> = t ) } is set
(A,(id (cod c))) . t is Morphism of (A,(cod (id (cod c)))) . t,(A,(dom (id (cod c)))) . t
(A,(cod (id (cod c)))) . t is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod (id (cod c)))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod (id (cod c))))) . t is Element of the carrier of (A)
(A,(dom (id (cod c)))) . t is Element of the carrier of (A)
Obj (A,(dom (id (cod c)))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom (id (cod c))))) . t is Element of the carrier of (A)
Hom ((cod (id (cod c))),t) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id (cod c)) & cod b<sub>1</sub> = t ) } is set
Hom ((dom (id (cod c))),t) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id (cod c)) & cod b<sub>1</sub> = t ) } is set
[(Hom ((cod (id (cod c))),t)),(Hom ((dom (id (cod c))),t))] is V1() set
{(Hom ((cod (id (cod c))),t)),(Hom ((dom (id (cod c))),t))} is non empty set
{(Hom ((cod (id (cod c))),t))} is non empty set
{{(Hom ((cod (id (cod c))),t)),(Hom ((dom (id (cod c))),t))},{(Hom ((cod (id (cod c))),t))}} is non empty set
id t is Morphism of t,t
hom ((id (cod c)),(id t)) is Relation-like Hom ((cod (id (cod c))),(dom (id t))) -defined Hom ((dom (id (cod c))),(cod (id t))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod (id (cod c))),(dom (id t)))),(Hom ((dom (id (cod c))),(cod (id t))))))
dom (id t) is Element of the carrier of A
the Source of A . (id t) is Element of the carrier of A
Hom ((cod (id (cod c))),(dom (id t))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id (cod c)) & cod b<sub>1</sub> = dom (id t) ) } is set
cod (id t) is Element of the carrier of A
the Target of A . (id t) is Element of the carrier of A
Hom ((dom (id (cod c))),(cod (id t))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id (cod c)) & cod b<sub>1</sub> = cod (id t) ) } is set
K33((Hom ((cod (id (cod c))),(dom (id t)))),(Hom ((dom (id (cod c))),(cod (id t))))) is Relation-like set
K32(K33((Hom ((cod (id (cod c))),(dom (id t)))),(Hom ((dom (id (cod c))),(cod (id t)))))) is set
[[(Hom ((cod (id (cod c))),t)),(Hom ((dom (id (cod c))),t))],(hom ((id (cod c)),(id t)))] is V1() set
{[(Hom ((cod (id (cod c))),t)),(Hom ((dom (id (cod c))),t))],(hom ((id (cod c)),(id t)))} is non empty set
{[(Hom ((cod (id (cod c))),t)),(Hom ((dom (id (cod c))),t))]} is non empty Relation-like Function-like set
{{[(Hom ((cod (id (cod c))),t)),(Hom ((dom (id (cod c))),t))],(hom ((id (cod c)),(id t)))},{[(Hom ((cod (id (cod c))),t)),(Hom ((dom (id (cod c))),t))]}} is non empty set
Hom ((cod c),t) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod c & cod b<sub>1</sub> = t ) } is set
[(Hom ((cod c),t)),(Hom ((dom (id (cod c))),t))] is V1() set
{(Hom ((cod c),t)),(Hom ((dom (id (cod c))),t))} is non empty set
{(Hom ((cod c),t))} is non empty set
{{(Hom ((cod c),t)),(Hom ((dom (id (cod c))),t))},{(Hom ((cod c),t))}} is non empty set
[[(Hom ((cod c),t)),(Hom ((dom (id (cod c))),t))],(hom ((id (cod c)),(id t)))] is V1() set
{[(Hom ((cod c),t)),(Hom ((dom (id (cod c))),t))],(hom ((id (cod c)),(id t)))} is non empty set
{[(Hom ((cod c),t)),(Hom ((dom (id (cod c))),t))]} is non empty Relation-like Function-like set
{{[(Hom ((cod c),t)),(Hom ((dom (id (cod c))),t))],(hom ((id (cod c)),(id t)))},{[(Hom ((cod c),t)),(Hom ((dom (id (cod c))),t))]}} is non empty set
[(Hom ((cod c),t)),(Hom ((cod c),t))] is V1() set
{(Hom ((cod c),t)),(Hom ((cod c),t))} is non empty set
{{(Hom ((cod c),t)),(Hom ((cod c),t))},{(Hom ((cod c),t))}} is non empty set
[[(Hom ((cod c),t)),(Hom ((cod c),t))],(hom ((id (cod c)),(id t)))] is V1() set
{[(Hom ((cod c),t)),(Hom ((cod c),t))],(hom ((id (cod c)),(id t)))} is non empty set
{[(Hom ((cod c),t)),(Hom ((cod c),t))]} is non empty Relation-like Function-like set
{{[(Hom ((cod c),t)),(Hom ((cod c),t))],(hom ((id (cod c)),(id t)))},{[(Hom ((cod c),t)),(Hom ((cod c),t))]}} is non empty set
hom ((cod c),(id t)) is Relation-like Hom ((cod c),(dom (id t))) -defined Hom ((cod c),(cod (id t))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod c),(dom (id t)))),(Hom ((cod c),(cod (id t))))))
Hom ((cod c),(dom (id t))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod c & cod b<sub>1</sub> = dom (id t) ) } is set
Hom ((cod c),(cod (id t))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod c & cod b<sub>1</sub> = cod (id t) ) } is set
K33((Hom ((cod c),(dom (id t)))),(Hom ((cod c),(cod (id t))))) is Relation-like set
K32(K33((Hom ((cod c),(dom (id t)))),(Hom ((cod c),(cod (id t)))))) is set
[[(Hom ((cod c),t)),(Hom ((cod c),t))],(hom ((cod c),(id t)))] is V1() set
{[(Hom ((cod c),t)),(Hom ((cod c),t))],(hom ((cod c),(id t)))} is non empty set
{{[(Hom ((cod c),t)),(Hom ((cod c),t))],(hom ((cod c),(id t)))},{[(Hom ((cod c),t)),(Hom ((cod c),t))]}} is non empty set
[(Hom ((cod c),t)),(Hom ((cod c),(cod (id t))))] is V1() set
{(Hom ((cod c),t)),(Hom ((cod c),(cod (id t))))} is non empty set
{{(Hom ((cod c),t)),(Hom ((cod c),(cod (id t))))},{(Hom ((cod c),t))}} is non empty set
[[(Hom ((cod c),t)),(Hom ((cod c),(cod (id t))))],(hom ((cod c),(id t)))] is V1() set
{[(Hom ((cod c),t)),(Hom ((cod c),(cod (id t))))],(hom ((cod c),(id t)))} is non empty set
{[(Hom ((cod c),t)),(Hom ((cod c),(cod (id t))))]} is non empty Relation-like Function-like set
{{[(Hom ((cod c),t)),(Hom ((cod c),(cod (id t))))],(hom ((cod c),(id t)))},{[(Hom ((cod c),t)),(Hom ((cod c),(cod (id t))))]}} is non empty set
[(Hom ((cod c),(dom (id t)))),(Hom ((cod c),(cod (id t))))] is V1() set
{(Hom ((cod c),(dom (id t)))),(Hom ((cod c),(cod (id t))))} is non empty set
{(Hom ((cod c),(dom (id t))))} is non empty set
{{(Hom ((cod c),(dom (id t)))),(Hom ((cod c),(cod (id t))))},{(Hom ((cod c),(dom (id t))))}} is non empty set
[[(Hom ((cod c),(dom (id t)))),(Hom ((cod c),(cod (id t))))],(hom ((cod c),(id t)))] is V1() set
{[(Hom ((cod c),(dom (id t)))),(Hom ((cod c),(cod (id t))))],(hom ((cod c),(id t)))} is non empty set
{[(Hom ((cod c),(dom (id t)))),(Hom ((cod c),(cod (id t))))]} is non empty Relation-like Function-like set
{{[(Hom ((cod c),(dom (id t)))),(Hom ((cod c),(cod (id t))))],(hom ((cod c),(id t)))},{[(Hom ((cod c),(dom (id t)))),(Hom ((cod c),(cod (id t))))]}} is non empty set
(A,(cod c)) . (id t) is set
(A,(cod c)) /. (id t) is Morphism of (A,(cod c)) . t,(A,(cod c)) . t
(A,(cod c)) . t is Element of the carrier of (A)
Obj (A,(cod c)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(cod c))) . t is Element of the carrier of (A)
id ((A,(cod c)) . t) is Morphism of (A,(cod c)) . t,(A,(cod c)) . t
(id (A,(cod c))) . t is Morphism of (A,(cod c)) . t,(A,(cod c)) . t
(id (A,(cod c))) . t is set
proj1 (id (A,(cod c))) is non empty set
[(A,(cod (id (cod c)))),(A,(dom (id (cod c))))] is V1() set
{(A,(cod (id (cod c)))),(A,(dom (id (cod c))))} is non empty functional set
{(A,(cod (id (cod c))))} is non empty functional set
{{(A,(cod (id (cod c)))),(A,(dom (id (cod c))))},{(A,(cod (id (cod c))))}} is non empty set
[[(A,(cod (id (cod c)))),(A,(dom (id (cod c))))],(A,(id (cod c)))] is V1() set
{[(A,(cod (id (cod c)))),(A,(dom (id (cod c))))],(A,(id (cod c)))} is non empty set
{[(A,(cod (id (cod c)))),(A,(dom (id (cod c))))]} is non empty Relation-like Function-like set
{{[(A,(cod (id (cod c)))),(A,(dom (id (cod c))))],(A,(id (cod c)))},{[(A,(cod (id (cod c)))),(A,(dom (id (cod c))))]}} is non empty set
[(A,(cod c)),(A,(dom (id (cod c))))] is V1() set
{(A,(cod c)),(A,(dom (id (cod c))))} is non empty functional set
{{(A,(cod c)),(A,(dom (id (cod c))))},{(A,(cod c))}} is non empty set
[[(A,(cod c)),(A,(dom (id (cod c))))],(A,(id (cod c)))] is V1() set
{[(A,(cod c)),(A,(dom (id (cod c))))],(A,(id (cod c)))} is non empty set
{[(A,(cod c)),(A,(dom (id (cod c))))]} is non empty Relation-like Function-like set
{{[(A,(cod c)),(A,(dom (id (cod c))))],(A,(id (cod c)))},{[(A,(cod c)),(A,(dom (id (cod c))))]}} is non empty set
[(A,(cod c)),(A,(cod c))] is V1() set
{(A,(cod c)),(A,(cod c))} is non empty functional set
{{(A,(cod c)),(A,(cod c))},{(A,(cod c))}} is non empty set
[[(A,(cod c)),(A,(cod c))],(A,(id (cod c)))] is V1() set
{[(A,(cod c)),(A,(cod c))],(A,(id (cod c)))} is non empty set
{[(A,(cod c)),(A,(cod c))]} is non empty Relation-like Function-like set
{{[(A,(cod c)),(A,(cod c))],(A,(id (cod c)))},{[(A,(cod c)),(A,(cod c))]}} is non empty set
the carrier of A is non empty set
the carrier of (Functors (A,(A))) is non empty set
c is Element of the carrier of A
id c is Morphism of c,c
F . (id c) is Element of the carrier' of (Functors (A,(A)))
(A,(id c)) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod (id c))),(A,(dom (id c)))
the carrier' of (A) is non empty set
cod (id c) is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Target of A . (id c) is Element of the carrier of A
(A,(cod (id c))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod (id c)) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
Maps (Hom A) is non empty set
K33( the carrier' of A,(Maps (Hom A))) is Relation-like set
K32(K33( the carrier' of A,(Maps (Hom A)))) is set
dom (id c) is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Source of A . (id c) is Element of the carrier of A
(A,(dom (id c))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom (id c)) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
proj1 (A,(id c)) is non empty set
(A,c) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- c is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
Funct (A,(A)) is non empty FUNCTOR-DOMAIN of A,(A)
g is Element of the carrier of (Functors (A,(A)))
id g is Morphism of g,g
id (A,c) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,c),(A,c)
F1 is set
(A,(id c)) . F1 is set
(id (A,c)) . F1 is set
F2 is Element of the carrier of A
id F2 is Morphism of F2,F2
Hom (F2,F2) is non empty Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = F2 & cod b<sub>1</sub> = F2 ) } is set
(A,(id c)) . F2 is Morphism of (A,(cod (id c))) . F2,(A,(dom (id c))) . F2
(A,(cod (id c))) . F2 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod (id c))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod (id c)))) . F2 is Element of the carrier of (A)
(A,(dom (id c))) . F2 is Element of the carrier of (A)
Obj (A,(dom (id c))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom (id c)))) . F2 is Element of the carrier of (A)
Hom ((cod (id c)),F2) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id c) & cod b<sub>1</sub> = F2 ) } is set
Hom ((dom (id c)),F2) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id c) & cod b<sub>1</sub> = F2 ) } is set
[(Hom ((cod (id c)),F2)),(Hom ((dom (id c)),F2))] is V1() set
{(Hom ((cod (id c)),F2)),(Hom ((dom (id c)),F2))} is non empty set
{(Hom ((cod (id c)),F2))} is non empty set
{{(Hom ((cod (id c)),F2)),(Hom ((dom (id c)),F2))},{(Hom ((cod (id c)),F2))}} is non empty set
hom ((id c),(id F2)) is Relation-like Hom ((cod (id c)),(dom (id F2))) -defined Hom ((dom (id c)),(cod (id F2))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod (id c)),(dom (id F2)))),(Hom ((dom (id c)),(cod (id F2))))))
dom (id F2) is Element of the carrier of A
the Source of A . (id F2) is Element of the carrier of A
Hom ((cod (id c)),(dom (id F2))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id c) & cod b<sub>1</sub> = dom (id F2) ) } is set
cod (id F2) is Element of the carrier of A
the Target of A . (id F2) is Element of the carrier of A
Hom ((dom (id c)),(cod (id F2))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id c) & cod b<sub>1</sub> = cod (id F2) ) } is set
K33((Hom ((cod (id c)),(dom (id F2)))),(Hom ((dom (id c)),(cod (id F2))))) is Relation-like set
K32(K33((Hom ((cod (id c)),(dom (id F2)))),(Hom ((dom (id c)),(cod (id F2)))))) is set
[[(Hom ((cod (id c)),F2)),(Hom ((dom (id c)),F2))],(hom ((id c),(id F2)))] is V1() set
{[(Hom ((cod (id c)),F2)),(Hom ((dom (id c)),F2))],(hom ((id c),(id F2)))} is non empty set
{[(Hom ((cod (id c)),F2)),(Hom ((dom (id c)),F2))]} is non empty Relation-like Function-like set
{{[(Hom ((cod (id c)),F2)),(Hom ((dom (id c)),F2))],(hom ((id c),(id F2)))},{[(Hom ((cod (id c)),F2)),(Hom ((dom (id c)),F2))]}} is non empty set
Hom (c,F2) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c & cod b<sub>1</sub> = F2 ) } is set
[(Hom (c,F2)),(Hom ((dom (id c)),F2))] is V1() set
{(Hom (c,F2)),(Hom ((dom (id c)),F2))} is non empty set
{(Hom (c,F2))} is non empty set
{{(Hom (c,F2)),(Hom ((dom (id c)),F2))},{(Hom (c,F2))}} is non empty set
[[(Hom (c,F2)),(Hom ((dom (id c)),F2))],(hom ((id c),(id F2)))] is V1() set
{[(Hom (c,F2)),(Hom ((dom (id c)),F2))],(hom ((id c),(id F2)))} is non empty set
{[(Hom (c,F2)),(Hom ((dom (id c)),F2))]} is non empty Relation-like Function-like set
{{[(Hom (c,F2)),(Hom ((dom (id c)),F2))],(hom ((id c),(id F2)))},{[(Hom (c,F2)),(Hom ((dom (id c)),F2))]}} is non empty set
[(Hom (c,F2)),(Hom (c,F2))] is V1() set
{(Hom (c,F2)),(Hom (c,F2))} is non empty set
{{(Hom (c,F2)),(Hom (c,F2))},{(Hom (c,F2))}} is non empty set
[[(Hom (c,F2)),(Hom (c,F2))],(hom ((id c),(id F2)))] is V1() set
{[(Hom (c,F2)),(Hom (c,F2))],(hom ((id c),(id F2)))} is non empty set
{[(Hom (c,F2)),(Hom (c,F2))]} is non empty Relation-like Function-like set
{{[(Hom (c,F2)),(Hom (c,F2))],(hom ((id c),(id F2)))},{[(Hom (c,F2)),(Hom (c,F2))]}} is non empty set
hom (c,(id F2)) is Relation-like Hom (c,(dom (id F2))) -defined Hom (c,(cod (id F2))) -valued Function-like quasi_total Element of K32(K33((Hom (c,(dom (id F2)))),(Hom (c,(cod (id F2))))))
Hom (c,(dom (id F2))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c & cod b<sub>1</sub> = dom (id F2) ) } is set
Hom (c,(cod (id F2))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c & cod b<sub>1</sub> = cod (id F2) ) } is set
K33((Hom (c,(dom (id F2)))),(Hom (c,(cod (id F2))))) is Relation-like set
K32(K33((Hom (c,(dom (id F2)))),(Hom (c,(cod (id F2)))))) is set
[[(Hom (c,F2)),(Hom (c,F2))],(hom (c,(id F2)))] is V1() set
{[(Hom (c,F2)),(Hom (c,F2))],(hom (c,(id F2)))} is non empty set
{{[(Hom (c,F2)),(Hom (c,F2))],(hom (c,(id F2)))},{[(Hom (c,F2)),(Hom (c,F2))]}} is non empty set
[(Hom (c,F2)),(Hom (c,(cod (id F2))))] is V1() set
{(Hom (c,F2)),(Hom (c,(cod (id F2))))} is non empty set
{{(Hom (c,F2)),(Hom (c,(cod (id F2))))},{(Hom (c,F2))}} is non empty set
[[(Hom (c,F2)),(Hom (c,(cod (id F2))))],(hom (c,(id F2)))] is V1() set
{[(Hom (c,F2)),(Hom (c,(cod (id F2))))],(hom (c,(id F2)))} is non empty set
{[(Hom (c,F2)),(Hom (c,(cod (id F2))))]} is non empty Relation-like Function-like set
{{[(Hom (c,F2)),(Hom (c,(cod (id F2))))],(hom (c,(id F2)))},{[(Hom (c,F2)),(Hom (c,(cod (id F2))))]}} is non empty set
[(Hom (c,(dom (id F2)))),(Hom (c,(cod (id F2))))] is V1() set
{(Hom (c,(dom (id F2)))),(Hom (c,(cod (id F2))))} is non empty set
{(Hom (c,(dom (id F2))))} is non empty set
{{(Hom (c,(dom (id F2)))),(Hom (c,(cod (id F2))))},{(Hom (c,(dom (id F2))))}} is non empty set
[[(Hom (c,(dom (id F2)))),(Hom (c,(cod (id F2))))],(hom (c,(id F2)))] is V1() set
{[(Hom (c,(dom (id F2)))),(Hom (c,(cod (id F2))))],(hom (c,(id F2)))} is non empty set
{[(Hom (c,(dom (id F2)))),(Hom (c,(cod (id F2))))]} is non empty Relation-like Function-like set
{{[(Hom (c,(dom (id F2)))),(Hom (c,(cod (id F2))))],(hom (c,(id F2)))},{[(Hom (c,(dom (id F2)))),(Hom (c,(cod (id F2))))]}} is non empty set
(A,c) . (id F2) is set
t is Morphism of F2,F2
(A,c) /. t is Morphism of (A,c) . F2,(A,c) . F2
(A,c) . F2 is Element of the carrier of (A)
Obj (A,c) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,c)) . F2 is Element of the carrier of (A)
id ((A,c) . F2) is Morphism of (A,c) . F2,(A,c) . F2
(id (A,c)) . F2 is Morphism of (A,c) . F2,(A,c) . F2
(id (A,c)) . F2 is set
proj1 (id (A,c)) is non empty set
[(A,(cod (id c))),(A,(dom (id c)))] is V1() set
{(A,(cod (id c))),(A,(dom (id c)))} is non empty functional set
{(A,(cod (id c)))} is non empty functional set
{{(A,(cod (id c))),(A,(dom (id c)))},{(A,(cod (id c)))}} is non empty set
[[(A,(cod (id c))),(A,(dom (id c)))],(A,(id c))] is V1() set
{[(A,(cod (id c))),(A,(dom (id c)))],(A,(id c))} is non empty set
{[(A,(cod (id c))),(A,(dom (id c)))]} is non empty Relation-like Function-like set
{{[(A,(cod (id c))),(A,(dom (id c)))],(A,(id c))},{[(A,(cod (id c))),(A,(dom (id c)))]}} is non empty set
[(A,c),(A,(dom (id c)))] is V1() set
{(A,c),(A,(dom (id c)))} is non empty functional set
{(A,c)} is non empty functional set
{{(A,c),(A,(dom (id c)))},{(A,c)}} is non empty set
[[(A,c),(A,(dom (id c)))],(A,(id c))] is V1() set
{[(A,c),(A,(dom (id c)))],(A,(id c))} is non empty set
{[(A,c),(A,(dom (id c)))]} is non empty Relation-like Function-like set
{{[(A,c),(A,(dom (id c)))],(A,(id c))},{[(A,c),(A,(dom (id c)))]}} is non empty set
[(A,c),(A,c)] is V1() set
{(A,c),(A,c)} is non empty functional set
{{(A,c),(A,c)},{(A,c)}} is non empty set
[[(A,c),(A,c)],(id (A,c))] is V1() set
{[(A,c),(A,c)],(id (A,c))} is non empty set
{[(A,c),(A,c)]} is non empty Relation-like Function-like set
{{[(A,c),(A,c)],(id (A,c))},{[(A,c),(A,c)]}} is non empty set
c is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (A,(A))) -valued Function-like V17( the carrier' of A) quasi_total Contravariant_Functor of A, Functors (A,(A))
c9 is Element of the carrier' of A
c . c9 is Element of the carrier' of (Functors (A,(A)))
cod c9 is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Target of A . c9 is Element of the carrier of A
(A,(cod c9)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
the carrier' of (A) is non empty set
hom?- (cod c9) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
Maps (Hom A) is non empty set
K33( the carrier' of A,(Maps (Hom A))) is Relation-like set
K32(K33( the carrier' of A,(Maps (Hom A)))) is set
dom c9 is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Source of A . c9 is Element of the carrier of A
(A,(dom c9)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom c9) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
[(A,(cod c9)),(A,(dom c9))] is V1() set
{(A,(cod c9)),(A,(dom c9))} is non empty functional set
{(A,(cod c9))} is non empty functional set
{{(A,(cod c9)),(A,(dom c9))},{(A,(cod c9))}} is non empty set
(A,c9) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod c9)),(A,(dom c9))
[[(A,(cod c9)),(A,(dom c9))],(A,c9)] is V1() set
{[(A,(cod c9)),(A,(dom c9))],(A,c9)} is non empty set
{[(A,(cod c9)),(A,(dom c9))]} is non empty Relation-like Function-like set
{{[(A,(cod c9)),(A,(dom c9))],(A,c9)},{[(A,(cod c9)),(A,(dom c9))]}} is non empty set
F is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (A,(A))) -valued Function-like V17( the carrier' of A) quasi_total Contravariant_Functor of A, Functors (A,(A))
c is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (A,(A))) -valued Function-like V17( the carrier' of A) quasi_total Contravariant_Functor of A, Functors (A,(A))
c9 is Element of the carrier' of A
F . c9 is Element of the carrier' of (Functors (A,(A)))
cod c9 is Element of the carrier of A
the carrier of A is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Target of A . c9 is Element of the carrier of A
(A,(cod c9)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
the carrier' of (A) is non empty set
hom?- (cod c9) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
Maps (Hom A) is non empty set
K33( the carrier' of A,(Maps (Hom A))) is Relation-like set
K32(K33( the carrier' of A,(Maps (Hom A)))) is set
dom c9 is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Source of A . c9 is Element of the carrier of A
(A,(dom c9)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom c9) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
[(A,(cod c9)),(A,(dom c9))] is V1() set
{(A,(cod c9)),(A,(dom c9))} is non empty functional set
{(A,(cod c9))} is non empty functional set
{{(A,(cod c9)),(A,(dom c9))},{(A,(cod c9))}} is non empty set
(A,c9) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod c9)),(A,(dom c9))
[[(A,(cod c9)),(A,(dom c9))],(A,c9)] is V1() set
{[(A,(cod c9)),(A,(dom c9))],(A,c9)} is non empty set
{[(A,(cod c9)),(A,(dom c9))]} is non empty Relation-like Function-like set
{{[(A,(cod c9)),(A,(dom c9))],(A,c9)},{[(A,(cod c9)),(A,(dom c9))]}} is non empty set
c . c9 is Element of the carrier' of (Functors (A,(A)))
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of A is non empty set
the carrier of F is non empty set
c is non empty Relation-like the carrier' of A -defined the carrier' of F -valued Function-like V17( the carrier' of A) quasi_total Contravariant_Functor of A,F
Obj c is non empty Relation-like the carrier of A -defined the carrier of F -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of F))
K33( the carrier of A, the carrier of F) is Relation-like set
K32(K33( the carrier of A, the carrier of F)) is set
c9 is Element of the carrier of A
(Obj c) . c9 is Element of the carrier of F
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
(A) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Hom A is non empty set
Ens (Hom A) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,(A)) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (A,(A))) is non empty set
F is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (A,(A))) -valued Function-like V17( the carrier' of A) quasi_total Functor of A, Functors (A,(A))
Obj F is non empty Relation-like the carrier of A -defined the carrier of (Functors (A,(A))) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Functors (A,(A)))))
the carrier of A is non empty set
the carrier of (Functors (A,(A))) is non empty set
K33( the carrier of A, the carrier of (Functors (A,(A)))) is Relation-like set
K32(K33( the carrier of A, the carrier of (Functors (A,(A))))) is set
proj1 F is non empty set
c is set
c9 is set
F . c is set
F . c9 is set
g is Element of the carrier' of A
dom g is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Source of A . g is Element of the carrier of A
cod g is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Target of A . g is Element of the carrier of A
F1 is Element of the carrier' of A
dom F1 is Element of the carrier of A
the Source of A . F1 is Element of the carrier of A
cod F1 is Element of the carrier of A
the Target of A . F1 is Element of the carrier of A
Hom ((dom g),(cod g)) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom g & cod b<sub>1</sub> = cod g ) } is set
F . (dom g) is Element of the carrier of (Functors (A,(A)))
(Obj F) . (dom g) is Element of the carrier of (Functors (A,(A)))
F . (cod g) is Element of the carrier of (Functors (A,(A)))
(Obj F) . (cod g) is Element of the carrier of (Functors (A,(A)))
Hom ((F . (dom g)),(F . (cod g))) is Element of K32( the carrier' of (Functors (A,(A))))
K32( the carrier' of (Functors (A,(A)))) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (Functors (A,(A))) : ( dom b<sub>1</sub> = F . (dom g) & cod b<sub>1</sub> = F . (cod g) ) } is set
Hom ((dom F1),(cod F1)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom F1 & cod b<sub>1</sub> = cod F1 ) } is set
F . (dom F1) is Element of the carrier of (Functors (A,(A)))
(Obj F) . (dom F1) is Element of the carrier of (Functors (A,(A)))
F . (cod F1) is Element of the carrier of (Functors (A,(A)))
(Obj F) . (cod F1) is Element of the carrier of (Functors (A,(A)))
Hom ((F . (dom F1)),(F . (cod F1))) is Element of K32( the carrier' of (Functors (A,(A))))
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (Functors (A,(A))) : ( dom b<sub>1</sub> = F . (dom F1) & cod b<sub>1</sub> = F . (cod F1) ) } is set
t is Morphism of dom g, cod g
F /. t is Morphism of F . (dom g),F . (cod g)
F . F1 is Element of the carrier' of (Functors (A,(A)))
t1 is Morphism of dom F1, cod F1
F /. t1 is Morphism of F . (dom F1),F . (cod F1)
dom (F /. t1) is Element of the carrier of (Functors (A,(A)))
the Source of (Functors (A,(A))) is non empty Relation-like the carrier' of (Functors (A,(A))) -defined the carrier of (Functors (A,(A))) -valued Function-like V17( the carrier' of (Functors (A,(A)))) quasi_total Element of K32(K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A)))))
K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A)))) is Relation-like set
K32(K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A))))) is set
the Source of (Functors (A,(A))) . (F /. t1) is Element of the carrier of (Functors (A,(A)))
cod (F /. t1) is Element of the carrier of (Functors (A,(A)))
the Target of (Functors (A,(A))) is non empty Relation-like the carrier' of (Functors (A,(A))) -defined the carrier of (Functors (A,(A))) -valued Function-like V17( the carrier' of (Functors (A,(A)))) quasi_total Element of K32(K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A)))))
the Target of (Functors (A,(A))) . (F /. t1) is Element of the carrier of (Functors (A,(A)))
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
(A) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Hom A is non empty set
Ens (Hom A) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,(A)) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (A,(A))) is non empty set
F is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (A,(A))) -valued Function-like V17( the carrier' of A) quasi_total Contravariant_Functor of A, Functors (A,(A))
Obj F is non empty Relation-like the carrier of A -defined the carrier of (Functors (A,(A))) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Functors (A,(A)))))
the carrier of A is non empty set
the carrier of (Functors (A,(A))) is non empty set
K33( the carrier of A, the carrier of (Functors (A,(A)))) is Relation-like set
K32(K33( the carrier of A, the carrier of (Functors (A,(A))))) is set
proj1 F is non empty set
c is set
c9 is set
F . c is set
F . c9 is set
g is Element of the carrier' of A
dom g is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Source of A . g is Element of the carrier of A
cod g is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Target of A . g is Element of the carrier of A
F1 is Element of the carrier' of A
dom F1 is Element of the carrier of A
the Source of A . F1 is Element of the carrier of A
cod F1 is Element of the carrier of A
the Target of A . F1 is Element of the carrier of A
(Obj F) . (dom g) is Element of the carrier of (Functors (A,(A)))
t is Morphism of dom F1, cod F1
F . t is Element of the carrier' of (Functors (A,(A)))
cod (F . t) is Element of the carrier of (Functors (A,(A)))
the Target of (Functors (A,(A))) is non empty Relation-like the carrier' of (Functors (A,(A))) -defined the carrier of (Functors (A,(A))) -valued Function-like V17( the carrier' of (Functors (A,(A)))) quasi_total Element of K32(K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A)))))
K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A)))) is Relation-like set
K32(K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A))))) is set
the Target of (Functors (A,(A))) . (F . t) is Element of the carrier of (Functors (A,(A)))
(Obj F) . (dom F1) is Element of the carrier of (Functors (A,(A)))
Hom ((dom g),(cod g)) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom g & cod b<sub>1</sub> = cod g ) } is set
(Obj F) . (cod g) is Element of the carrier of (Functors (A,(A)))
dom (F . t) is Element of the carrier of (Functors (A,(A)))
the Source of (Functors (A,(A))) is non empty Relation-like the carrier' of (Functors (A,(A))) -defined the carrier of (Functors (A,(A))) -valued Function-like V17( the carrier' of (Functors (A,(A)))) quasi_total Element of K32(K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A)))))
the Source of (Functors (A,(A))) . (F . t) is Element of the carrier of (Functors (A,(A)))
(Obj F) . (cod F1) is Element of the carrier of (Functors (A,(A)))
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
(A) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Hom A is non empty set
Ens (Hom A) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,(A)) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
(A) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (A,(A))) -valued Function-like V17( the carrier' of A) quasi_total Contravariant_Functor of A, Functors (A,(A))
the carrier' of A is non empty set
the carrier' of (Functors (A,(A))) is non empty set
the carrier of A is non empty set
c is Element of the carrier of A
c9 is Element of the carrier of A
Hom (c,c9) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c & cod b<sub>1</sub> = c9 ) } is set
g is Morphism of c,c9
(A) . g is Element of the carrier' of (Functors (A,(A)))
F1 is Morphism of c,c9
(A) . F1 is Element of the carrier' of (Functors (A,(A)))
cod g is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Target of A . g is Element of the carrier of A
(A,(cod g)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
the carrier' of (A) is non empty set
hom?- (cod g) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
Maps (Hom A) is non empty set
K33( the carrier' of A,(Maps (Hom A))) is Relation-like set
K32(K33( the carrier' of A,(Maps (Hom A)))) is set
dom g is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Source of A . g is Element of the carrier of A
(A,(dom g)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom g) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
[(A,(cod g)),(A,(dom g))] is V1() set
{(A,(cod g)),(A,(dom g))} is non empty functional set
{(A,(cod g))} is non empty functional set
{{(A,(cod g)),(A,(dom g))},{(A,(cod g))}} is non empty set
(A,g) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod g)),(A,(dom g))
[[(A,(cod g)),(A,(dom g))],(A,g)] is V1() set
{[(A,(cod g)),(A,(dom g))],(A,g)} is non empty set
{[(A,(cod g)),(A,(dom g))]} is non empty Relation-like Function-like set
{{[(A,(cod g)),(A,(dom g))],(A,g)},{[(A,(cod g)),(A,(dom g))]}} is non empty set
cod F1 is Element of the carrier of A
the Target of A . F1 is Element of the carrier of A
(A,(cod F1)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod F1) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
dom F1 is Element of the carrier of A
the Source of A . F1 is Element of the carrier of A
(A,(dom F1)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom F1) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
[(A,(cod F1)),(A,(dom F1))] is V1() set
{(A,(cod F1)),(A,(dom F1))} is non empty functional set
{(A,(cod F1))} is non empty functional set
{{(A,(cod F1)),(A,(dom F1))},{(A,(cod F1))}} is non empty set
(A,F1) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod F1)),(A,(dom F1))
[[(A,(cod F1)),(A,(dom F1))],(A,F1)] is V1() set
{[(A,(cod F1)),(A,(dom F1))],(A,F1)} is non empty set
{[(A,(cod F1)),(A,(dom F1))]} is non empty Relation-like Function-like set
{{[(A,(cod F1)),(A,(dom F1))],(A,F1)},{[(A,(cod F1)),(A,(dom F1))]}} is non empty set
[(A,(cod g)),(A,(dom g)),(A,g)] is V1() V2() set
[(A,(cod F1)),(A,(dom F1)),(A,F1)] is V1() V2() set
Hom ((cod g),c9) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod g & cod b<sub>1</sub> = c9 ) } is set
Hom ((dom g),c9) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom g & cod b<sub>1</sub> = c9 ) } is set
[(Hom ((cod g),c9)),(Hom ((dom g),c9))] is V1() set
{(Hom ((cod g),c9)),(Hom ((dom g),c9))} is non empty set
{(Hom ((cod g),c9))} is non empty set
{{(Hom ((cod g),c9)),(Hom ((dom g),c9))},{(Hom ((cod g),c9))}} is non empty set
id c9 is Morphism of c9,c9
hom (g,(id c9)) is Relation-like Hom ((cod g),(dom (id c9))) -defined Hom ((dom g),(cod (id c9))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod g),(dom (id c9)))),(Hom ((dom g),(cod (id c9))))))
dom (id c9) is Element of the carrier of A
the Source of A . (id c9) is Element of the carrier of A
Hom ((cod g),(dom (id c9))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod g & cod b<sub>1</sub> = dom (id c9) ) } is set
cod (id c9) is Element of the carrier of A
the Target of A . (id c9) is Element of the carrier of A
Hom ((dom g),(cod (id c9))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom g & cod b<sub>1</sub> = cod (id c9) ) } is set
K33((Hom ((cod g),(dom (id c9)))),(Hom ((dom g),(cod (id c9))))) is Relation-like set
K32(K33((Hom ((cod g),(dom (id c9)))),(Hom ((dom g),(cod (id c9)))))) is set
[[(Hom ((cod g),c9)),(Hom ((dom g),c9))],(hom (g,(id c9)))] is V1() set
{[(Hom ((cod g),c9)),(Hom ((dom g),c9))],(hom (g,(id c9)))} is non empty set
{[(Hom ((cod g),c9)),(Hom ((dom g),c9))]} is non empty Relation-like Function-like set
{{[(Hom ((cod g),c9)),(Hom ((dom g),c9))],(hom (g,(id c9)))},{[(Hom ((cod g),c9)),(Hom ((dom g),c9))]}} is non empty set
(A,F1) . c9 is Morphism of (A,(cod F1)) . c9,(A,(dom F1)) . c9
(A,(cod F1)) . c9 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod F1)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod F1))) . c9 is Element of the carrier of (A)
(A,(dom F1)) . c9 is Element of the carrier of (A)
Obj (A,(dom F1)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom F1))) . c9 is Element of the carrier of (A)
Hom ((cod F1),c9) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod F1 & cod b<sub>1</sub> = c9 ) } is set
Hom ((dom F1),c9) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom F1 & cod b<sub>1</sub> = c9 ) } is set
[(Hom ((cod F1),c9)),(Hom ((dom F1),c9))] is V1() set
{(Hom ((cod F1),c9)),(Hom ((dom F1),c9))} is non empty set
{(Hom ((cod F1),c9))} is non empty set
{{(Hom ((cod F1),c9)),(Hom ((dom F1),c9))},{(Hom ((cod F1),c9))}} is non empty set
hom (F1,(id c9)) is Relation-like Hom ((cod F1),(dom (id c9))) -defined Hom ((dom F1),(cod (id c9))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod F1),(dom (id c9)))),(Hom ((dom F1),(cod (id c9))))))
Hom ((cod F1),(dom (id c9))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod F1 & cod b<sub>1</sub> = dom (id c9) ) } is set
Hom ((dom F1),(cod (id c9))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom F1 & cod b<sub>1</sub> = cod (id c9) ) } is set
K33((Hom ((cod F1),(dom (id c9)))),(Hom ((dom F1),(cod (id c9))))) is Relation-like set
K32(K33((Hom ((cod F1),(dom (id c9)))),(Hom ((dom F1),(cod (id c9)))))) is set
[[(Hom ((cod F1),c9)),(Hom ((dom F1),c9))],(hom (F1,(id c9)))] is V1() set
{[(Hom ((cod F1),c9)),(Hom ((dom F1),c9))],(hom (F1,(id c9)))} is non empty set
{[(Hom ((cod F1),c9)),(Hom ((dom F1),c9))]} is non empty Relation-like Function-like set
{{[(Hom ((cod F1),c9)),(Hom ((dom F1),c9))],(hom (F1,(id c9)))},{[(Hom ((cod F1),c9)),(Hom ((dom F1),c9))]}} is non empty set
Hom (c9,c9) is non empty Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c9 & cod b<sub>1</sub> = c9 ) } is set
[(Hom (c9,c9)),(Hom ((dom g),c9))] is V1() set
{(Hom (c9,c9)),(Hom ((dom g),c9))} is non empty set
{(Hom (c9,c9))} is non empty set
{{(Hom (c9,c9)),(Hom ((dom g),c9))},{(Hom (c9,c9))}} is non empty set
[[(Hom (c9,c9)),(Hom ((dom g),c9))],(hom (g,(id c9)))] is V1() set
{[(Hom (c9,c9)),(Hom ((dom g),c9))],(hom (g,(id c9)))} is non empty set
{[(Hom (c9,c9)),(Hom ((dom g),c9))]} is non empty Relation-like Function-like set
{{[(Hom (c9,c9)),(Hom ((dom g),c9))],(hom (g,(id c9)))},{[(Hom (c9,c9)),(Hom ((dom g),c9))]}} is non empty set
[(Hom (c9,c9)),(Hom (c,c9))] is V1() set
{(Hom (c9,c9)),(Hom (c,c9))} is non empty set
{{(Hom (c9,c9)),(Hom (c,c9))},{(Hom (c9,c9))}} is non empty set
[[(Hom (c9,c9)),(Hom (c,c9))],(hom (g,(id c9)))] is V1() set
{[(Hom (c9,c9)),(Hom (c,c9))],(hom (g,(id c9)))} is non empty set
{[(Hom (c9,c9)),(Hom (c,c9))]} is non empty Relation-like Function-like set
{{[(Hom (c9,c9)),(Hom (c,c9))],(hom (g,(id c9)))},{[(Hom (c9,c9)),(Hom (c,c9))]}} is non empty set
[(Hom (c9,c9)),(Hom ((dom F1),c9))] is V1() set
{(Hom (c9,c9)),(Hom ((dom F1),c9))} is non empty set
{{(Hom (c9,c9)),(Hom ((dom F1),c9))},{(Hom (c9,c9))}} is non empty set
[[(Hom (c9,c9)),(Hom ((dom F1),c9))],(hom (F1,(id c9)))] is V1() set
{[(Hom (c9,c9)),(Hom ((dom F1),c9))],(hom (F1,(id c9)))} is non empty set
{[(Hom (c9,c9)),(Hom ((dom F1),c9))]} is non empty Relation-like Function-like set
{{[(Hom (c9,c9)),(Hom ((dom F1),c9))],(hom (F1,(id c9)))},{[(Hom (c9,c9)),(Hom ((dom F1),c9))]}} is non empty set
[[(Hom (c9,c9)),(Hom (c,c9))],(hom (F1,(id c9)))] is V1() set
{[(Hom (c9,c9)),(Hom (c,c9))],(hom (F1,(id c9)))} is non empty set
{{[(Hom (c9,c9)),(Hom (c,c9))],(hom (F1,(id c9)))},{[(Hom (c9,c9)),(Hom (c,c9))]}} is non empty set
[(Hom (c9,c9)),(Hom (c,c9)),(hom (F1,(id c9)))] is V1() V2() set
[(Hom (c9,c9)),(Hom (c,c9)),(hom (g,(id c9)))] is V1() V2() set
F2 is Element of the carrier' of A
(id c9) (*) F2 is Element of the carrier' of A
(id c9) * (id c9) is Morphism of c9,c9
(hom (F1,(id c9))) . F2 is set
((id c9) * (id c9)) (*) F1 is Element of the carrier' of A
(id c9) (*) F1 is Element of the carrier' of A
(id c9) * F1 is Morphism of c,c9
(hom (g,(id c9))) . F2 is set
((id c9) * (id c9)) (*) g is Element of the carrier' of A
(id c9) (*) g is Element of the carrier' of A
(id c9) * g is Morphism of c,c9
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
(A) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (A,(A))) -valued Function-like V17( the carrier' of A) quasi_total (A, Functors (A,(A))) Contravariant_Functor of A, Functors (A,(A))
the carrier' of A is non empty set
(A) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Hom A is non empty set
Ens (Hom A) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,(A)) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (A,(A))) is non empty set
Obj (A) is non empty Relation-like the carrier of A -defined the carrier of (Functors (A,(A))) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Functors (A,(A)))))
the carrier of A is non empty set
the carrier of (Functors (A,(A))) is non empty set
K33( the carrier of A, the carrier of (Functors (A,(A)))) is Relation-like set
K32(K33( the carrier of A, the carrier of (Functors (A,(A))))) is set
proj1 (Obj (A)) is non empty set
c is set
c9 is set
(Obj (A)) . c is set
(Obj (A)) . c9 is set
F1 is Element of the carrier of A
id F1 is Morphism of F1,F1
Hom (F1,F1) is non empty Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = F1 & cod b<sub>1</sub> = F1 ) } is set
(A,F1) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
the carrier' of (A) is non empty set
hom?- F1 is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
Maps (Hom A) is non empty set
K33( the carrier' of A,(Maps (Hom A))) is Relation-like set
K32(K33( the carrier' of A,(Maps (Hom A)))) is set
Funct (A,(A)) is non empty FUNCTOR-DOMAIN of A,(A)
g is Element of the carrier of A
(A,g) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- g is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
(A) . (id F1) is Element of the carrier' of (Functors (A,(A)))
t is Element of the carrier of (Functors (A,(A)))
id t is Morphism of t,t
(A,(id F1)) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod (id F1))),(A,(dom (id F1)))
cod (id F1) is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Target of A . (id F1) is Element of the carrier of A
(A,(cod (id F1))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod (id F1)) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
dom (id F1) is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Source of A . (id F1) is Element of the carrier of A
(A,(dom (id F1))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom (id F1)) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
proj1 (A,(id F1)) is non empty set
id (A,F1) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,F1),(A,F1)
t is set
(A,(id F1)) . t is set
(id (A,F1)) . t is set
t1 is Element of the carrier of A
id t1 is Morphism of t1,t1
Hom (t1,t1) is non empty Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = t1 & cod b<sub>1</sub> = t1 ) } is set
(A,(id F1)) . t1 is Morphism of (A,(cod (id F1))) . t1,(A,(dom (id F1))) . t1
(A,(cod (id F1))) . t1 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod (id F1))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod (id F1)))) . t1 is Element of the carrier of (A)
(A,(dom (id F1))) . t1 is Element of the carrier of (A)
Obj (A,(dom (id F1))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom (id F1)))) . t1 is Element of the carrier of (A)
Hom ((cod (id F1)),t1) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id F1) & cod b<sub>1</sub> = t1 ) } is set
Hom ((dom (id F1)),t1) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id F1) & cod b<sub>1</sub> = t1 ) } is set
[(Hom ((cod (id F1)),t1)),(Hom ((dom (id F1)),t1))] is V1() set
{(Hom ((cod (id F1)),t1)),(Hom ((dom (id F1)),t1))} is non empty set
{(Hom ((cod (id F1)),t1))} is non empty set
{{(Hom ((cod (id F1)),t1)),(Hom ((dom (id F1)),t1))},{(Hom ((cod (id F1)),t1))}} is non empty set
hom ((id F1),(id t1)) is Relation-like Hom ((cod (id F1)),(dom (id t1))) -defined Hom ((dom (id F1)),(cod (id t1))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod (id F1)),(dom (id t1)))),(Hom ((dom (id F1)),(cod (id t1))))))
dom (id t1) is Element of the carrier of A
the Source of A . (id t1) is Element of the carrier of A
Hom ((cod (id F1)),(dom (id t1))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id F1) & cod b<sub>1</sub> = dom (id t1) ) } is set
cod (id t1) is Element of the carrier of A
the Target of A . (id t1) is Element of the carrier of A
Hom ((dom (id F1)),(cod (id t1))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id F1) & cod b<sub>1</sub> = cod (id t1) ) } is set
K33((Hom ((cod (id F1)),(dom (id t1)))),(Hom ((dom (id F1)),(cod (id t1))))) is Relation-like set
K32(K33((Hom ((cod (id F1)),(dom (id t1)))),(Hom ((dom (id F1)),(cod (id t1)))))) is set
[[(Hom ((cod (id F1)),t1)),(Hom ((dom (id F1)),t1))],(hom ((id F1),(id t1)))] is V1() set
{[(Hom ((cod (id F1)),t1)),(Hom ((dom (id F1)),t1))],(hom ((id F1),(id t1)))} is non empty set
{[(Hom ((cod (id F1)),t1)),(Hom ((dom (id F1)),t1))]} is non empty Relation-like Function-like set
{{[(Hom ((cod (id F1)),t1)),(Hom ((dom (id F1)),t1))],(hom ((id F1),(id t1)))},{[(Hom ((cod (id F1)),t1)),(Hom ((dom (id F1)),t1))]}} is non empty set
Hom (F1,t1) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = F1 & cod b<sub>1</sub> = t1 ) } is set
[(Hom (F1,t1)),(Hom ((dom (id F1)),t1))] is V1() set
{(Hom (F1,t1)),(Hom ((dom (id F1)),t1))} is non empty set
{(Hom (F1,t1))} is non empty set
{{(Hom (F1,t1)),(Hom ((dom (id F1)),t1))},{(Hom (F1,t1))}} is non empty set
[[(Hom (F1,t1)),(Hom ((dom (id F1)),t1))],(hom ((id F1),(id t1)))] is V1() set
{[(Hom (F1,t1)),(Hom ((dom (id F1)),t1))],(hom ((id F1),(id t1)))} is non empty set
{[(Hom (F1,t1)),(Hom ((dom (id F1)),t1))]} is non empty Relation-like Function-like set
{{[(Hom (F1,t1)),(Hom ((dom (id F1)),t1))],(hom ((id F1),(id t1)))},{[(Hom (F1,t1)),(Hom ((dom (id F1)),t1))]}} is non empty set
[(Hom (F1,t1)),(Hom (F1,t1))] is V1() set
{(Hom (F1,t1)),(Hom (F1,t1))} is non empty set
{{(Hom (F1,t1)),(Hom (F1,t1))},{(Hom (F1,t1))}} is non empty set
[[(Hom (F1,t1)),(Hom (F1,t1))],(hom ((id F1),(id t1)))] is V1() set
{[(Hom (F1,t1)),(Hom (F1,t1))],(hom ((id F1),(id t1)))} is non empty set
{[(Hom (F1,t1)),(Hom (F1,t1))]} is non empty Relation-like Function-like set
{{[(Hom (F1,t1)),(Hom (F1,t1))],(hom ((id F1),(id t1)))},{[(Hom (F1,t1)),(Hom (F1,t1))]}} is non empty set
hom (F1,(id t1)) is Relation-like Hom (F1,(dom (id t1))) -defined Hom (F1,(cod (id t1))) -valued Function-like quasi_total Element of K32(K33((Hom (F1,(dom (id t1)))),(Hom (F1,(cod (id t1))))))
Hom (F1,(dom (id t1))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = F1 & cod b<sub>1</sub> = dom (id t1) ) } is set
Hom (F1,(cod (id t1))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = F1 & cod b<sub>1</sub> = cod (id t1) ) } is set
K33((Hom (F1,(dom (id t1)))),(Hom (F1,(cod (id t1))))) is Relation-like set
K32(K33((Hom (F1,(dom (id t1)))),(Hom (F1,(cod (id t1)))))) is set
[[(Hom (F1,t1)),(Hom (F1,t1))],(hom (F1,(id t1)))] is V1() set
{[(Hom (F1,t1)),(Hom (F1,t1))],(hom (F1,(id t1)))} is non empty set
{{[(Hom (F1,t1)),(Hom (F1,t1))],(hom (F1,(id t1)))},{[(Hom (F1,t1)),(Hom (F1,t1))]}} is non empty set
[(Hom (F1,t1)),(Hom (F1,(cod (id t1))))] is V1() set
{(Hom (F1,t1)),(Hom (F1,(cod (id t1))))} is non empty set
{{(Hom (F1,t1)),(Hom (F1,(cod (id t1))))},{(Hom (F1,t1))}} is non empty set
[[(Hom (F1,t1)),(Hom (F1,(cod (id t1))))],(hom (F1,(id t1)))] is V1() set
{[(Hom (F1,t1)),(Hom (F1,(cod (id t1))))],(hom (F1,(id t1)))} is non empty set
{[(Hom (F1,t1)),(Hom (F1,(cod (id t1))))]} is non empty Relation-like Function-like set
{{[(Hom (F1,t1)),(Hom (F1,(cod (id t1))))],(hom (F1,(id t1)))},{[(Hom (F1,t1)),(Hom (F1,(cod (id t1))))]}} is non empty set
[(Hom (F1,(dom (id t1)))),(Hom (F1,(cod (id t1))))] is V1() set
{(Hom (F1,(dom (id t1)))),(Hom (F1,(cod (id t1))))} is non empty set
{(Hom (F1,(dom (id t1))))} is non empty set
{{(Hom (F1,(dom (id t1)))),(Hom (F1,(cod (id t1))))},{(Hom (F1,(dom (id t1))))}} is non empty set
[[(Hom (F1,(dom (id t1)))),(Hom (F1,(cod (id t1))))],(hom (F1,(id t1)))] is V1() set
{[(Hom (F1,(dom (id t1)))),(Hom (F1,(cod (id t1))))],(hom (F1,(id t1)))} is non empty set
{[(Hom (F1,(dom (id t1)))),(Hom (F1,(cod (id t1))))]} is non empty Relation-like Function-like set
{{[(Hom (F1,(dom (id t1)))),(Hom (F1,(cod (id t1))))],(hom (F1,(id t1)))},{[(Hom (F1,(dom (id t1)))),(Hom (F1,(cod (id t1))))]}} is non empty set
(A,F1) . (id t1) is set
f is Morphism of t1,t1
(A,F1) /. f is Morphism of (A,F1) . t1,(A,F1) . t1
(A,F1) . t1 is Element of the carrier of (A)
Obj (A,F1) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,F1)) . t1 is Element of the carrier of (A)
id ((A,F1) . t1) is Morphism of (A,F1) . t1,(A,F1) . t1
(id (A,F1)) . t1 is Morphism of (A,F1) . t1,(A,F1) . t1
(id (A,F1)) . t1 is set
proj1 (id (A,F1)) is non empty set
[(A,(cod (id F1))),(A,(dom (id F1)))] is V1() set
{(A,(cod (id F1))),(A,(dom (id F1)))} is non empty functional set
{(A,(cod (id F1)))} is non empty functional set
{{(A,(cod (id F1))),(A,(dom (id F1)))},{(A,(cod (id F1)))}} is non empty set
[[(A,(cod (id F1))),(A,(dom (id F1)))],(A,(id F1))] is V1() set
{[(A,(cod (id F1))),(A,(dom (id F1)))],(A,(id F1))} is non empty set
{[(A,(cod (id F1))),(A,(dom (id F1)))]} is non empty Relation-like Function-like set
{{[(A,(cod (id F1))),(A,(dom (id F1)))],(A,(id F1))},{[(A,(cod (id F1))),(A,(dom (id F1)))]}} is non empty set
[(A,F1),(A,(dom (id F1)))] is V1() set
{(A,F1),(A,(dom (id F1)))} is non empty functional set
{(A,F1)} is non empty functional set
{{(A,F1),(A,(dom (id F1)))},{(A,F1)}} is non empty set
[[(A,F1),(A,(dom (id F1)))],(A,(id F1))] is V1() set
{[(A,F1),(A,(dom (id F1)))],(A,(id F1))} is non empty set
{[(A,F1),(A,(dom (id F1)))]} is non empty Relation-like Function-like set
{{[(A,F1),(A,(dom (id F1)))],(A,(id F1))},{[(A,F1),(A,(dom (id F1)))]}} is non empty set
[(A,F1),(A,F1)] is V1() set
{(A,F1),(A,F1)} is non empty functional set
{{(A,F1),(A,F1)},{(A,F1)}} is non empty set
[[(A,F1),(A,F1)],(id (A,F1))] is V1() set
{[(A,F1),(A,F1)],(id (A,F1))} is non empty set
{[(A,F1),(A,F1)]} is non empty Relation-like Function-like set
{{[(A,F1),(A,F1)],(id (A,F1))},{[(A,F1),(A,F1)]}} is non empty set
(Obj (A)) . F1 is Element of the carrier of (Functors (A,(A)))
id g is Morphism of g,g
(A) . (id g) is Element of the carrier' of (Functors (A,(A)))
d1 is Element of the carrier of (Functors (A,(A)))
id d1 is Morphism of d1,d1
(A,(id g)) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod (id g))),(A,(dom (id g)))
cod (id g) is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Target of A . (id g) is Element of the carrier of A
(A,(cod (id g))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod (id g)) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
dom (id g) is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Source of A . (id g) is Element of the carrier of A
(A,(dom (id g))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom (id g)) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
proj1 (A,(id g)) is non empty set
id (A,g) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,g),(A,g)
t is set
(A,(id g)) . t is set
(id (A,g)) . t is set
t1 is Element of the carrier of A
id t1 is Morphism of t1,t1
Hom (t1,t1) is non empty Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = t1 & cod b<sub>1</sub> = t1 ) } is set
(A,(id g)) . t1 is Morphism of (A,(cod (id g))) . t1,(A,(dom (id g))) . t1
(A,(cod (id g))) . t1 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,(cod (id g))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,(cod (id g)))) . t1 is Element of the carrier of (A)
(A,(dom (id g))) . t1 is Element of the carrier of (A)
Obj (A,(dom (id g))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom (id g)))) . t1 is Element of the carrier of (A)
Hom ((cod (id g)),t1) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id g) & cod b<sub>1</sub> = t1 ) } is set
Hom ((dom (id g)),t1) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id g) & cod b<sub>1</sub> = t1 ) } is set
[(Hom ((cod (id g)),t1)),(Hom ((dom (id g)),t1))] is V1() set
{(Hom ((cod (id g)),t1)),(Hom ((dom (id g)),t1))} is non empty set
{(Hom ((cod (id g)),t1))} is non empty set
{{(Hom ((cod (id g)),t1)),(Hom ((dom (id g)),t1))},{(Hom ((cod (id g)),t1))}} is non empty set
hom ((id g),(id t1)) is Relation-like Hom ((cod (id g)),(dom (id t1))) -defined Hom ((dom (id g)),(cod (id t1))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod (id g)),(dom (id t1)))),(Hom ((dom (id g)),(cod (id t1))))))
dom (id t1) is Element of the carrier of A
the Source of A . (id t1) is Element of the carrier of A
Hom ((cod (id g)),(dom (id t1))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id g) & cod b<sub>1</sub> = dom (id t1) ) } is set
cod (id t1) is Element of the carrier of A
the Target of A . (id t1) is Element of the carrier of A
Hom ((dom (id g)),(cod (id t1))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id g) & cod b<sub>1</sub> = cod (id t1) ) } is set
K33((Hom ((cod (id g)),(dom (id t1)))),(Hom ((dom (id g)),(cod (id t1))))) is Relation-like set
K32(K33((Hom ((cod (id g)),(dom (id t1)))),(Hom ((dom (id g)),(cod (id t1)))))) is set
[[(Hom ((cod (id g)),t1)),(Hom ((dom (id g)),t1))],(hom ((id g),(id t1)))] is V1() set
{[(Hom ((cod (id g)),t1)),(Hom ((dom (id g)),t1))],(hom ((id g),(id t1)))} is non empty set
{[(Hom ((cod (id g)),t1)),(Hom ((dom (id g)),t1))]} is non empty Relation-like Function-like set
{{[(Hom ((cod (id g)),t1)),(Hom ((dom (id g)),t1))],(hom ((id g),(id t1)))},{[(Hom ((cod (id g)),t1)),(Hom ((dom (id g)),t1))]}} is non empty set
Hom (g,t1) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = g & cod b<sub>1</sub> = t1 ) } is set
[(Hom (g,t1)),(Hom ((dom (id g)),t1))] is V1() set
{(Hom (g,t1)),(Hom ((dom (id g)),t1))} is non empty set
{(Hom (g,t1))} is non empty set
{{(Hom (g,t1)),(Hom ((dom (id g)),t1))},{(Hom (g,t1))}} is non empty set
[[(Hom (g,t1)),(Hom ((dom (id g)),t1))],(hom ((id g),(id t1)))] is V1() set
{[(Hom (g,t1)),(Hom ((dom (id g)),t1))],(hom ((id g),(id t1)))} is non empty set
{[(Hom (g,t1)),(Hom ((dom (id g)),t1))]} is non empty Relation-like Function-like set
{{[(Hom (g,t1)),(Hom ((dom (id g)),t1))],(hom ((id g),(id t1)))},{[(Hom (g,t1)),(Hom ((dom (id g)),t1))]}} is non empty set
[(Hom (g,t1)),(Hom (g,t1))] is V1() set
{(Hom (g,t1)),(Hom (g,t1))} is non empty set
{{(Hom (g,t1)),(Hom (g,t1))},{(Hom (g,t1))}} is non empty set
[[(Hom (g,t1)),(Hom (g,t1))],(hom ((id g),(id t1)))] is V1() set
{[(Hom (g,t1)),(Hom (g,t1))],(hom ((id g),(id t1)))} is non empty set
{[(Hom (g,t1)),(Hom (g,t1))]} is non empty Relation-like Function-like set
{{[(Hom (g,t1)),(Hom (g,t1))],(hom ((id g),(id t1)))},{[(Hom (g,t1)),(Hom (g,t1))]}} is non empty set
hom (g,(id t1)) is Relation-like Hom (g,(dom (id t1))) -defined Hom (g,(cod (id t1))) -valued Function-like quasi_total Element of K32(K33((Hom (g,(dom (id t1)))),(Hom (g,(cod (id t1))))))
Hom (g,(dom (id t1))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = g & cod b<sub>1</sub> = dom (id t1) ) } is set
Hom (g,(cod (id t1))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = g & cod b<sub>1</sub> = cod (id t1) ) } is set
K33((Hom (g,(dom (id t1)))),(Hom (g,(cod (id t1))))) is Relation-like set
K32(K33((Hom (g,(dom (id t1)))),(Hom (g,(cod (id t1)))))) is set
[[(Hom (g,t1)),(Hom (g,t1))],(hom (g,(id t1)))] is V1() set
{[(Hom (g,t1)),(Hom (g,t1))],(hom (g,(id t1)))} is non empty set
{{[(Hom (g,t1)),(Hom (g,t1))],(hom (g,(id t1)))},{[(Hom (g,t1)),(Hom (g,t1))]}} is non empty set
[(Hom (g,t1)),(Hom (g,(cod (id t1))))] is V1() set
{(Hom (g,t1)),(Hom (g,(cod (id t1))))} is non empty set
{{(Hom (g,t1)),(Hom (g,(cod (id t1))))},{(Hom (g,t1))}} is non empty set
[[(Hom (g,t1)),(Hom (g,(cod (id t1))))],(hom (g,(id t1)))] is V1() set
{[(Hom (g,t1)),(Hom (g,(cod (id t1))))],(hom (g,(id t1)))} is non empty set
{[(Hom (g,t1)),(Hom (g,(cod (id t1))))]} is non empty Relation-like Function-like set
{{[(Hom (g,t1)),(Hom (g,(cod (id t1))))],(hom (g,(id t1)))},{[(Hom (g,t1)),(Hom (g,(cod (id t1))))]}} is non empty set
[(Hom (g,(dom (id t1)))),(Hom (g,(cod (id t1))))] is V1() set
{(Hom (g,(dom (id t1)))),(Hom (g,(cod (id t1))))} is non empty set
{(Hom (g,(dom (id t1))))} is non empty set
{{(Hom (g,(dom (id t1)))),(Hom (g,(cod (id t1))))},{(Hom (g,(dom (id t1))))}} is non empty set
[[(Hom (g,(dom (id t1)))),(Hom (g,(cod (id t1))))],(hom (g,(id t1)))] is V1() set
{[(Hom (g,(dom (id t1)))),(Hom (g,(cod (id t1))))],(hom (g,(id t1)))} is non empty set
{[(Hom (g,(dom (id t1)))),(Hom (g,(cod (id t1))))]} is non empty Relation-like Function-like set
{{[(Hom (g,(dom (id t1)))),(Hom (g,(cod (id t1))))],(hom (g,(id t1)))},{[(Hom (g,(dom (id t1)))),(Hom (g,(cod (id t1))))]}} is non empty set
(A,g) . (id t1) is set
f is Morphism of t1,t1
(A,g) /. f is Morphism of (A,g) . t1,(A,g) . t1
(A,g) . t1 is Element of the carrier of (A)
Obj (A,g) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,g)) . t1 is Element of the carrier of (A)
id ((A,g) . t1) is Morphism of (A,g) . t1,(A,g) . t1
(id (A,g)) . t1 is Morphism of (A,g) . t1,(A,g) . t1
(id (A,g)) . t1 is set
proj1 (id (A,g)) is non empty set
[(A,(cod (id g))),(A,(dom (id g)))] is V1() set
{(A,(cod (id g))),(A,(dom (id g)))} is non empty functional set
{(A,(cod (id g)))} is non empty functional set
{{(A,(cod (id g))),(A,(dom (id g)))},{(A,(cod (id g)))}} is non empty set
[[(A,(cod (id g))),(A,(dom (id g)))],(A,(id g))] is V1() set
{[(A,(cod (id g))),(A,(dom (id g)))],(A,(id g))} is non empty set
{[(A,(cod (id g))),(A,(dom (id g)))]} is non empty Relation-like Function-like set
{{[(A,(cod (id g))),(A,(dom (id g)))],(A,(id g))},{[(A,(cod (id g))),(A,(dom (id g)))]}} is non empty set
[(A,g),(A,(dom (id g)))] is V1() set
{(A,g),(A,(dom (id g)))} is non empty functional set
{(A,g)} is non empty functional set
{{(A,g),(A,(dom (id g)))},{(A,g)}} is non empty set
[[(A,g),(A,(dom (id g)))],(A,(id g))] is V1() set
{[(A,g),(A,(dom (id g)))],(A,(id g))} is non empty set
{[(A,g),(A,(dom (id g)))]} is non empty Relation-like Function-like set
{{[(A,g),(A,(dom (id g)))],(A,(id g))},{[(A,g),(A,(dom (id g)))]}} is non empty set
[(A,g),(A,g)] is V1() set
{(A,g),(A,g)} is non empty functional set
{{(A,g),(A,g)},{(A,g)}} is non empty set
[[(A,g),(A,g)],(id (A,g))] is V1() set
{[(A,g),(A,g)],(id (A,g))} is non empty set
{[(A,g),(A,g)]} is non empty Relation-like Function-like set
{{[(A,g),(A,g)],(id (A,g))},{[(A,g),(A,g)]}} is non empty set
(Obj (A)) . g is Element of the carrier of (Functors (A,(A)))
F2 is Morphism of F1,F1
dom F2 is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Source of A . F2 is Element of the carrier of A
Hom (g,(dom F2)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = g & cod b<sub>1</sub> = dom F2 ) } is set
cod F2 is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Target of A . F2 is Element of the carrier of A
Hom (g,(cod F2)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = g & cod b<sub>1</sub> = cod F2 ) } is set
[(Hom (g,(dom F2))),(Hom (g,(cod F2)))] is V1() set
{(Hom (g,(dom F2))),(Hom (g,(cod F2)))} is non empty set
{(Hom (g,(dom F2)))} is non empty set
{{(Hom (g,(dom F2))),(Hom (g,(cod F2)))},{(Hom (g,(dom F2)))}} is non empty set
hom (g,F2) is Relation-like Hom (g,(dom F2)) -defined Hom (g,(cod F2)) -valued Function-like quasi_total Element of K32(K33((Hom (g,(dom F2))),(Hom (g,(cod F2)))))
K33((Hom (g,(dom F2))),(Hom (g,(cod F2)))) is Relation-like set
K32(K33((Hom (g,(dom F2))),(Hom (g,(cod F2))))) is set
[[(Hom (g,(dom F2))),(Hom (g,(cod F2)))],(hom (g,F2))] is V1() set
{[(Hom (g,(dom F2))),(Hom (g,(cod F2)))],(hom (g,F2))} is non empty set
{[(Hom (g,(dom F2))),(Hom (g,(cod F2)))]} is non empty Relation-like Function-like set
{{[(Hom (g,(dom F2))),(Hom (g,(cod F2)))],(hom (g,F2))},{[(Hom (g,(dom F2))),(Hom (g,(cod F2)))]}} is non empty set
(hom?- F1) . F2 is Element of Maps (Hom A)
Hom (F1,(dom F2)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = F1 & cod b<sub>1</sub> = dom F2 ) } is set
Hom (F1,(cod F2)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = F1 & cod b<sub>1</sub> = cod F2 ) } is set
[(Hom (F1,(dom F2))),(Hom (F1,(cod F2)))] is V1() set
{(Hom (F1,(dom F2))),(Hom (F1,(cod F2)))} is non empty set
{(Hom (F1,(dom F2)))} is non empty set
{{(Hom (F1,(dom F2))),(Hom (F1,(cod F2)))},{(Hom (F1,(dom F2)))}} is non empty set
hom (F1,F2) is Relation-like Hom (F1,(dom F2)) -defined Hom (F1,(cod F2)) -valued Function-like quasi_total Element of K32(K33((Hom (F1,(dom F2))),(Hom (F1,(cod F2)))))
K33((Hom (F1,(dom F2))),(Hom (F1,(cod F2)))) is Relation-like set
K32(K33((Hom (F1,(dom F2))),(Hom (F1,(cod F2))))) is set
[[(Hom (F1,(dom F2))),(Hom (F1,(cod F2)))],(hom (F1,F2))] is V1() set
{[(Hom (F1,(dom F2))),(Hom (F1,(cod F2)))],(hom (F1,F2))} is non empty set
{[(Hom (F1,(dom F2))),(Hom (F1,(cod F2)))]} is non empty Relation-like Function-like set
{{[(Hom (F1,(dom F2))),(Hom (F1,(cod F2)))],(hom (F1,F2))},{[(Hom (F1,(dom F2))),(Hom (F1,(cod F2)))]}} is non empty set
[(Hom (g,(dom F2))),(Hom (g,(cod F2))),(hom (g,F2))] is V1() V2() set
[(Hom (F1,(dom F2))),(Hom (F1,(cod F2))),(hom (F1,F2))] is V1() V2() set
Hom (g,F1) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = g & cod b<sub>1</sub> = F1 ) } is set
d is Morphism of g,F1
dom d is Element of the carrier of A
the Source of A . d is Element of the carrier of A
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
(A) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Hom A is non empty set
Ens (Hom A) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,(A)) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
(A) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (A,(A))) -valued Function-like one-to-one V17( the carrier' of A) quasi_total (A, Functors (A,(A))) Contravariant_Functor of A, Functors (A,(A))
the carrier' of A is non empty set
the carrier' of (Functors (A,(A))) is non empty set
the carrier of A is non empty set
c9 is Element of the carrier of A
(A,(Functors (A,(A))),(A),c9) is Element of the carrier of (Functors (A,(A)))
the carrier of (Functors (A,(A))) is non empty set
Obj (A) is non empty Relation-like the carrier of A -defined the carrier of (Functors (A,(A))) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Functors (A,(A)))))
K33( the carrier of A, the carrier of (Functors (A,(A)))) is Relation-like set
K32(K33( the carrier of A, the carrier of (Functors (A,(A))))) is set
(Obj (A)) . c9 is Element of the carrier of (Functors (A,(A)))
c is Element of the carrier of A
(A,(Functors (A,(A))),(A),c) is Element of the carrier of (Functors (A,(A)))
(Obj (A)) . c is Element of the carrier of (Functors (A,(A)))
Hom ((A,(Functors (A,(A))),(A),c9),(A,(Functors (A,(A))),(A),c)) is Element of K32( the carrier' of (Functors (A,(A))))
K32( the carrier' of (Functors (A,(A)))) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (Functors (A,(A))) : ( dom b<sub>1</sub> = (A,(Functors (A,(A))),(A),c9) & cod b<sub>1</sub> = (A,(Functors (A,(A))),(A),c) ) } is set
Hom (c,c9) is Element of K32( the carrier' of A)
K32( the carrier' of A) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c & cod b<sub>1</sub> = c9 ) } is set
(A,c9) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
the carrier' of (A) is non empty set
hom?- c9 is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
Maps (Hom A) is non empty set
K33( the carrier' of A,(Maps (Hom A))) is Relation-like set
K32(K33( the carrier' of A,(Maps (Hom A)))) is set
(A,c9) . c9 is Element of the carrier of (A)
the carrier of (A) is non empty set
Obj (A,c9) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
K33( the carrier of A, the carrier of (A)) is Relation-like set
K32(K33( the carrier of A, the carrier of (A))) is set
(Obj (A,c9)) . c9 is Element of the carrier of (A)
hom?- ((Hom A),c9) is non empty Relation-like the carrier' of A -defined the carrier' of (Ens (Hom A)) -valued Function-like V17( the carrier' of A) quasi_total Functor of A, Ens (Hom A)
the carrier' of (Ens (Hom A)) is non empty set
(hom?- ((Hom A),c9)) . c9 is Element of the carrier of (Ens (Hom A))
the carrier of (Ens (Hom A)) is non empty set
Obj (hom?- ((Hom A),c9)) is non empty Relation-like the carrier of A -defined the carrier of (Ens (Hom A)) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Ens (Hom A))))
K33( the carrier of A, the carrier of (Ens (Hom A))) is Relation-like set
K32(K33( the carrier of A, the carrier of (Ens (Hom A)))) is set
(Obj (hom?- ((Hom A),c9))) . c9 is Element of the carrier of (Ens (Hom A))
Hom (c9,c9) is non empty Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c9 & cod b<sub>1</sub> = c9 ) } is set
g is Morphism of (A,(Functors (A,(A))),(A),c9),(A,(Functors (A,(A))),(A),c)
NatTrans (A,(A)) is non empty NatTrans-DOMAIN of A,(A)
F1 is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
F2 is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
[F1,F2] is V1() set
{F1,F2} is non empty functional set
{F1} is non empty functional set
{{F1,F2},{F1}} is non empty set
t is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of F1,F2
[[F1,F2],t] is V1() set
{[F1,F2],t} is non empty set
{[F1,F2]} is non empty Relation-like Function-like set
{{[F1,F2],t},{[F1,F2]}} is non empty set
dom g is Element of the carrier of (Functors (A,(A)))
the Source of (Functors (A,(A))) is non empty Relation-like the carrier' of (Functors (A,(A))) -defined the carrier of (Functors (A,(A))) -valued Function-like V17( the carrier' of (Functors (A,(A)))) quasi_total Element of K32(K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A)))))
K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A)))) is Relation-like set
K32(K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A))))) is set
the Source of (Functors (A,(A))) . g is Element of the carrier of (Functors (A,(A)))
Funct (A,(A)) is non empty FUNCTOR-DOMAIN of A,(A)
(A,c) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- c is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
id c is Morphism of c,c
(A) . (id c) is Element of the carrier' of (Functors (A,(A)))
d is Element of the carrier of (Functors (A,(A)))
id d is Morphism of d,d
(A,(id c)) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod (id c))),(A,(dom (id c)))
cod (id c) is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Target of A . (id c) is Element of the carrier of A
(A,(cod (id c))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod (id c)) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
dom (id c) is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Source of A . (id c) is Element of the carrier of A
(A,(dom (id c))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom (id c)) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
proj1 (A,(id c)) is non empty set
id (A,c) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,c),(A,c)
t1 is set
(A,(id c)) . t1 is set
(id (A,c)) . t1 is set
f is Element of the carrier of A
id f is Morphism of f,f
Hom (f,f) is non empty Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = f & cod b<sub>1</sub> = f ) } is set
(A,(id c)) . f is Morphism of (A,(cod (id c))) . f,(A,(dom (id c))) . f
(A,(cod (id c))) . f is Element of the carrier of (A)
Obj (A,(cod (id c))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(cod (id c)))) . f is Element of the carrier of (A)
(A,(dom (id c))) . f is Element of the carrier of (A)
Obj (A,(dom (id c))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom (id c)))) . f is Element of the carrier of (A)
Hom ((cod (id c)),f) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id c) & cod b<sub>1</sub> = f ) } is set
Hom ((dom (id c)),f) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id c) & cod b<sub>1</sub> = f ) } is set
[(Hom ((cod (id c)),f)),(Hom ((dom (id c)),f))] is V1() set
{(Hom ((cod (id c)),f)),(Hom ((dom (id c)),f))} is non empty set
{(Hom ((cod (id c)),f))} is non empty set
{{(Hom ((cod (id c)),f)),(Hom ((dom (id c)),f))},{(Hom ((cod (id c)),f))}} is non empty set
hom ((id c),(id f)) is Relation-like Hom ((cod (id c)),(dom (id f))) -defined Hom ((dom (id c)),(cod (id f))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod (id c)),(dom (id f)))),(Hom ((dom (id c)),(cod (id f))))))
dom (id f) is Element of the carrier of A
the Source of A . (id f) is Element of the carrier of A
Hom ((cod (id c)),(dom (id f))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id c) & cod b<sub>1</sub> = dom (id f) ) } is set
cod (id f) is Element of the carrier of A
the Target of A . (id f) is Element of the carrier of A
Hom ((dom (id c)),(cod (id f))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id c) & cod b<sub>1</sub> = cod (id f) ) } is set
K33((Hom ((cod (id c)),(dom (id f)))),(Hom ((dom (id c)),(cod (id f))))) is Relation-like set
K32(K33((Hom ((cod (id c)),(dom (id f)))),(Hom ((dom (id c)),(cod (id f)))))) is set
[[(Hom ((cod (id c)),f)),(Hom ((dom (id c)),f))],(hom ((id c),(id f)))] is V1() set
{[(Hom ((cod (id c)),f)),(Hom ((dom (id c)),f))],(hom ((id c),(id f)))} is non empty set
{[(Hom ((cod (id c)),f)),(Hom ((dom (id c)),f))]} is non empty Relation-like Function-like set
{{[(Hom ((cod (id c)),f)),(Hom ((dom (id c)),f))],(hom ((id c),(id f)))},{[(Hom ((cod (id c)),f)),(Hom ((dom (id c)),f))]}} is non empty set
Hom (c,f) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c & cod b<sub>1</sub> = f ) } is set
[(Hom (c,f)),(Hom ((dom (id c)),f))] is V1() set
{(Hom (c,f)),(Hom ((dom (id c)),f))} is non empty set
{(Hom (c,f))} is non empty set
{{(Hom (c,f)),(Hom ((dom (id c)),f))},{(Hom (c,f))}} is non empty set
[[(Hom (c,f)),(Hom ((dom (id c)),f))],(hom ((id c),(id f)))] is V1() set
{[(Hom (c,f)),(Hom ((dom (id c)),f))],(hom ((id c),(id f)))} is non empty set
{[(Hom (c,f)),(Hom ((dom (id c)),f))]} is non empty Relation-like Function-like set
{{[(Hom (c,f)),(Hom ((dom (id c)),f))],(hom ((id c),(id f)))},{[(Hom (c,f)),(Hom ((dom (id c)),f))]}} is non empty set
[(Hom (c,f)),(Hom (c,f))] is V1() set
{(Hom (c,f)),(Hom (c,f))} is non empty set
{{(Hom (c,f)),(Hom (c,f))},{(Hom (c,f))}} is non empty set
[[(Hom (c,f)),(Hom (c,f))],(hom ((id c),(id f)))] is V1() set
{[(Hom (c,f)),(Hom (c,f))],(hom ((id c),(id f)))} is non empty set
{[(Hom (c,f)),(Hom (c,f))]} is non empty Relation-like Function-like set
{{[(Hom (c,f)),(Hom (c,f))],(hom ((id c),(id f)))},{[(Hom (c,f)),(Hom (c,f))]}} is non empty set
hom (c,(id f)) is Relation-like Hom (c,(dom (id f))) -defined Hom (c,(cod (id f))) -valued Function-like quasi_total Element of K32(K33((Hom (c,(dom (id f)))),(Hom (c,(cod (id f))))))
Hom (c,(dom (id f))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c & cod b<sub>1</sub> = dom (id f) ) } is set
Hom (c,(cod (id f))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c & cod b<sub>1</sub> = cod (id f) ) } is set
K33((Hom (c,(dom (id f)))),(Hom (c,(cod (id f))))) is Relation-like set
K32(K33((Hom (c,(dom (id f)))),(Hom (c,(cod (id f)))))) is set
[[(Hom (c,f)),(Hom (c,f))],(hom (c,(id f)))] is V1() set
{[(Hom (c,f)),(Hom (c,f))],(hom (c,(id f)))} is non empty set
{{[(Hom (c,f)),(Hom (c,f))],(hom (c,(id f)))},{[(Hom (c,f)),(Hom (c,f))]}} is non empty set
[(Hom (c,f)),(Hom (c,(cod (id f))))] is V1() set
{(Hom (c,f)),(Hom (c,(cod (id f))))} is non empty set
{{(Hom (c,f)),(Hom (c,(cod (id f))))},{(Hom (c,f))}} is non empty set
[[(Hom (c,f)),(Hom (c,(cod (id f))))],(hom (c,(id f)))] is V1() set
{[(Hom (c,f)),(Hom (c,(cod (id f))))],(hom (c,(id f)))} is non empty set
{[(Hom (c,f)),(Hom (c,(cod (id f))))]} is non empty Relation-like Function-like set
{{[(Hom (c,f)),(Hom (c,(cod (id f))))],(hom (c,(id f)))},{[(Hom (c,f)),(Hom (c,(cod (id f))))]}} is non empty set
[(Hom (c,(dom (id f)))),(Hom (c,(cod (id f))))] is V1() set
{(Hom (c,(dom (id f)))),(Hom (c,(cod (id f))))} is non empty set
{(Hom (c,(dom (id f))))} is non empty set
{{(Hom (c,(dom (id f)))),(Hom (c,(cod (id f))))},{(Hom (c,(dom (id f))))}} is non empty set
[[(Hom (c,(dom (id f)))),(Hom (c,(cod (id f))))],(hom (c,(id f)))] is V1() set
{[(Hom (c,(dom (id f)))),(Hom (c,(cod (id f))))],(hom (c,(id f)))} is non empty set
{[(Hom (c,(dom (id f)))),(Hom (c,(cod (id f))))]} is non empty Relation-like Function-like set
{{[(Hom (c,(dom (id f)))),(Hom (c,(cod (id f))))],(hom (c,(id f)))},{[(Hom (c,(dom (id f)))),(Hom (c,(cod (id f))))]}} is non empty set
(A,c) . (id f) is set
a is Morphism of f,f
(A,c) /. a is Morphism of (A,c) . f,(A,c) . f
(A,c) . f is Element of the carrier of (A)
Obj (A,c) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,c)) . f is Element of the carrier of (A)
id ((A,c) . f) is Morphism of (A,c) . f,(A,c) . f
(id (A,c)) . f is Morphism of (A,c) . f,(A,c) . f
(id (A,c)) . f is set
proj1 (id (A,c)) is non empty set
[(A,(cod (id c))),(A,(dom (id c)))] is V1() set
{(A,(cod (id c))),(A,(dom (id c)))} is non empty functional set
{(A,(cod (id c)))} is non empty functional set
{{(A,(cod (id c))),(A,(dom (id c)))},{(A,(cod (id c)))}} is non empty set
[[(A,(cod (id c))),(A,(dom (id c)))],(A,(id c))] is V1() set
{[(A,(cod (id c))),(A,(dom (id c)))],(A,(id c))} is non empty set
{[(A,(cod (id c))),(A,(dom (id c)))]} is non empty Relation-like Function-like set
{{[(A,(cod (id c))),(A,(dom (id c)))],(A,(id c))},{[(A,(cod (id c))),(A,(dom (id c)))]}} is non empty set
[(A,c),(A,(dom (id c)))] is V1() set
{(A,c),(A,(dom (id c)))} is non empty functional set
{(A,c)} is non empty functional set
{{(A,c),(A,(dom (id c)))},{(A,c)}} is non empty set
[[(A,c),(A,(dom (id c)))],(A,(id c))] is V1() set
{[(A,c),(A,(dom (id c)))],(A,(id c))} is non empty set
{[(A,c),(A,(dom (id c)))]} is non empty Relation-like Function-like set
{{[(A,c),(A,(dom (id c)))],(A,(id c))},{[(A,c),(A,(dom (id c)))]}} is non empty set
[(A,c),(A,c)] is V1() set
{(A,c),(A,c)} is non empty functional set
{{(A,c),(A,c)},{(A,c)}} is non empty set
[[(A,c),(A,c)],(id (A,c))] is V1() set
{[(A,c),(A,c)],(id (A,c))} is non empty set
{[(A,c),(A,c)]} is non empty Relation-like Function-like set
{{[(A,c),(A,c)],(id (A,c))},{[(A,c),(A,c)]}} is non empty set
id c9 is Morphism of c9,c9
(A) . (id c9) is Element of the carrier' of (Functors (A,(A)))
d1 is Element of the carrier of (Functors (A,(A)))
id d1 is Morphism of d1,d1
(A,(id c9)) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod (id c9))),(A,(dom (id c9)))
cod (id c9) is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Target of A . (id c9) is Element of the carrier of A
(A,(cod (id c9))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod (id c9)) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
dom (id c9) is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Source of A . (id c9) is Element of the carrier of A
(A,(dom (id c9))) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom (id c9)) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
proj1 (A,(id c9)) is non empty set
id (A,c9) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,c9),(A,c9)
t1 is set
(A,(id c9)) . t1 is set
(id (A,c9)) . t1 is set
f is Element of the carrier of A
id f is Morphism of f,f
Hom (f,f) is non empty Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = f & cod b<sub>1</sub> = f ) } is set
(A,(id c9)) . f is Morphism of (A,(cod (id c9))) . f,(A,(dom (id c9))) . f
(A,(cod (id c9))) . f is Element of the carrier of (A)
Obj (A,(cod (id c9))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(cod (id c9)))) . f is Element of the carrier of (A)
(A,(dom (id c9))) . f is Element of the carrier of (A)
Obj (A,(dom (id c9))) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom (id c9)))) . f is Element of the carrier of (A)
Hom ((cod (id c9)),f) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id c9) & cod b<sub>1</sub> = f ) } is set
Hom ((dom (id c9)),f) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id c9) & cod b<sub>1</sub> = f ) } is set
[(Hom ((cod (id c9)),f)),(Hom ((dom (id c9)),f))] is V1() set
{(Hom ((cod (id c9)),f)),(Hom ((dom (id c9)),f))} is non empty set
{(Hom ((cod (id c9)),f))} is non empty set
{{(Hom ((cod (id c9)),f)),(Hom ((dom (id c9)),f))},{(Hom ((cod (id c9)),f))}} is non empty set
hom ((id c9),(id f)) is Relation-like Hom ((cod (id c9)),(dom (id f))) -defined Hom ((dom (id c9)),(cod (id f))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod (id c9)),(dom (id f)))),(Hom ((dom (id c9)),(cod (id f))))))
dom (id f) is Element of the carrier of A
the Source of A . (id f) is Element of the carrier of A
Hom ((cod (id c9)),(dom (id f))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = cod (id c9) & cod b<sub>1</sub> = dom (id f) ) } is set
cod (id f) is Element of the carrier of A
the Target of A . (id f) is Element of the carrier of A
Hom ((dom (id c9)),(cod (id f))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = dom (id c9) & cod b<sub>1</sub> = cod (id f) ) } is set
K33((Hom ((cod (id c9)),(dom (id f)))),(Hom ((dom (id c9)),(cod (id f))))) is Relation-like set
K32(K33((Hom ((cod (id c9)),(dom (id f)))),(Hom ((dom (id c9)),(cod (id f)))))) is set
[[(Hom ((cod (id c9)),f)),(Hom ((dom (id c9)),f))],(hom ((id c9),(id f)))] is V1() set
{[(Hom ((cod (id c9)),f)),(Hom ((dom (id c9)),f))],(hom ((id c9),(id f)))} is non empty set
{[(Hom ((cod (id c9)),f)),(Hom ((dom (id c9)),f))]} is non empty Relation-like Function-like set
{{[(Hom ((cod (id c9)),f)),(Hom ((dom (id c9)),f))],(hom ((id c9),(id f)))},{[(Hom ((cod (id c9)),f)),(Hom ((dom (id c9)),f))]}} is non empty set
Hom (c9,f) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c9 & cod b<sub>1</sub> = f ) } is set
[(Hom (c9,f)),(Hom ((dom (id c9)),f))] is V1() set
{(Hom (c9,f)),(Hom ((dom (id c9)),f))} is non empty set
{(Hom (c9,f))} is non empty set
{{(Hom (c9,f)),(Hom ((dom (id c9)),f))},{(Hom (c9,f))}} is non empty set
[[(Hom (c9,f)),(Hom ((dom (id c9)),f))],(hom ((id c9),(id f)))] is V1() set
{[(Hom (c9,f)),(Hom ((dom (id c9)),f))],(hom ((id c9),(id f)))} is non empty set
{[(Hom (c9,f)),(Hom ((dom (id c9)),f))]} is non empty Relation-like Function-like set
{{[(Hom (c9,f)),(Hom ((dom (id c9)),f))],(hom ((id c9),(id f)))},{[(Hom (c9,f)),(Hom ((dom (id c9)),f))]}} is non empty set
[(Hom (c9,f)),(Hom (c9,f))] is V1() set
{(Hom (c9,f)),(Hom (c9,f))} is non empty set
{{(Hom (c9,f)),(Hom (c9,f))},{(Hom (c9,f))}} is non empty set
[[(Hom (c9,f)),(Hom (c9,f))],(hom ((id c9),(id f)))] is V1() set
{[(Hom (c9,f)),(Hom (c9,f))],(hom ((id c9),(id f)))} is non empty set
{[(Hom (c9,f)),(Hom (c9,f))]} is non empty Relation-like Function-like set
{{[(Hom (c9,f)),(Hom (c9,f))],(hom ((id c9),(id f)))},{[(Hom (c9,f)),(Hom (c9,f))]}} is non empty set
hom (c9,(id f)) is Relation-like Hom (c9,(dom (id f))) -defined Hom (c9,(cod (id f))) -valued Function-like quasi_total Element of K32(K33((Hom (c9,(dom (id f)))),(Hom (c9,(cod (id f))))))
Hom (c9,(dom (id f))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c9 & cod b<sub>1</sub> = dom (id f) ) } is set
Hom (c9,(cod (id f))) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c9 & cod b<sub>1</sub> = cod (id f) ) } is set
K33((Hom (c9,(dom (id f)))),(Hom (c9,(cod (id f))))) is Relation-like set
K32(K33((Hom (c9,(dom (id f)))),(Hom (c9,(cod (id f)))))) is set
[[(Hom (c9,f)),(Hom (c9,f))],(hom (c9,(id f)))] is V1() set
{[(Hom (c9,f)),(Hom (c9,f))],(hom (c9,(id f)))} is non empty set
{{[(Hom (c9,f)),(Hom (c9,f))],(hom (c9,(id f)))},{[(Hom (c9,f)),(Hom (c9,f))]}} is non empty set
[(Hom (c9,f)),(Hom (c9,(cod (id f))))] is V1() set
{(Hom (c9,f)),(Hom (c9,(cod (id f))))} is non empty set
{{(Hom (c9,f)),(Hom (c9,(cod (id f))))},{(Hom (c9,f))}} is non empty set
[[(Hom (c9,f)),(Hom (c9,(cod (id f))))],(hom (c9,(id f)))] is V1() set
{[(Hom (c9,f)),(Hom (c9,(cod (id f))))],(hom (c9,(id f)))} is non empty set
{[(Hom (c9,f)),(Hom (c9,(cod (id f))))]} is non empty Relation-like Function-like set
{{[(Hom (c9,f)),(Hom (c9,(cod (id f))))],(hom (c9,(id f)))},{[(Hom (c9,f)),(Hom (c9,(cod (id f))))]}} is non empty set
[(Hom (c9,(dom (id f)))),(Hom (c9,(cod (id f))))] is V1() set
{(Hom (c9,(dom (id f)))),(Hom (c9,(cod (id f))))} is non empty set
{(Hom (c9,(dom (id f))))} is non empty set
{{(Hom (c9,(dom (id f)))),(Hom (c9,(cod (id f))))},{(Hom (c9,(dom (id f))))}} is non empty set
[[(Hom (c9,(dom (id f)))),(Hom (c9,(cod (id f))))],(hom (c9,(id f)))] is V1() set
{[(Hom (c9,(dom (id f)))),(Hom (c9,(cod (id f))))],(hom (c9,(id f)))} is non empty set
{[(Hom (c9,(dom (id f)))),(Hom (c9,(cod (id f))))]} is non empty Relation-like Function-like set
{{[(Hom (c9,(dom (id f)))),(Hom (c9,(cod (id f))))],(hom (c9,(id f)))},{[(Hom (c9,(dom (id f)))),(Hom (c9,(cod (id f))))]}} is non empty set
(A,c9) . (id f) is set
a is Morphism of f,f
(A,c9) /. a is Morphism of (A,c9) . f,(A,c9) . f
(A,c9) . f is Element of the carrier of (A)
(Obj (A,c9)) . f is Element of the carrier of (A)
id ((A,c9) . f) is Morphism of (A,c9) . f,(A,c9) . f
(id (A,c9)) . f is Morphism of (A,c9) . f,(A,c9) . f
(id (A,c9)) . f is set
proj1 (id (A,c9)) is non empty set
[(A,(cod (id c9))),(A,(dom (id c9)))] is V1() set
{(A,(cod (id c9))),(A,(dom (id c9)))} is non empty functional set
{(A,(cod (id c9)))} is non empty functional set
{{(A,(cod (id c9))),(A,(dom (id c9)))},{(A,(cod (id c9)))}} is non empty set
[[(A,(cod (id c9))),(A,(dom (id c9)))],(A,(id c9))] is V1() set
{[(A,(cod (id c9))),(A,(dom (id c9)))],(A,(id c9))} is non empty set
{[(A,(cod (id c9))),(A,(dom (id c9)))]} is non empty Relation-like Function-like set
{{[(A,(cod (id c9))),(A,(dom (id c9)))],(A,(id c9))},{[(A,(cod (id c9))),(A,(dom (id c9)))]}} is non empty set
[(A,c9),(A,(dom (id c9)))] is V1() set
{(A,c9),(A,(dom (id c9)))} is non empty functional set
{(A,c9)} is non empty functional set
{{(A,c9),(A,(dom (id c9)))},{(A,c9)}} is non empty set
[[(A,c9),(A,(dom (id c9)))],(A,(id c9))] is V1() set
{[(A,c9),(A,(dom (id c9)))],(A,(id c9))} is non empty set
{[(A,c9),(A,(dom (id c9)))]} is non empty Relation-like Function-like set
{{[(A,c9),(A,(dom (id c9)))],(A,(id c9))},{[(A,c9),(A,(dom (id c9)))]}} is non empty set
[(A,c9),(A,c9)] is V1() set
{(A,c9),(A,c9)} is non empty functional set
{{(A,c9),(A,c9)},{(A,c9)}} is non empty set
[[(A,c9),(A,c9)],(id (A,c9))] is V1() set
{[(A,c9),(A,c9)],(id (A,c9))} is non empty set
{[(A,c9),(A,c9)]} is non empty Relation-like Function-like set
{{[(A,c9),(A,c9)],(id (A,c9))},{[(A,c9),(A,c9)]}} is non empty set
cod g is Element of the carrier of (Functors (A,(A)))
the Target of (Functors (A,(A))) is non empty Relation-like the carrier' of (Functors (A,(A))) -defined the carrier of (Functors (A,(A))) -valued Function-like V17( the carrier' of (Functors (A,(A)))) quasi_total Element of K32(K33( the carrier' of (Functors (A,(A))), the carrier of (Functors (A,(A)))))
the Target of (Functors (A,(A))) . g is Element of the carrier of (Functors (A,(A)))
(A,c) . c9 is Element of the carrier of (A)
Obj (A,c) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,c)) . c9 is Element of the carrier of (A)
hom?- ((Hom A),c) is non empty Relation-like the carrier' of A -defined the carrier' of (Ens (Hom A)) -valued Function-like V17( the carrier' of A) quasi_total Functor of A, Ens (Hom A)
(hom?- ((Hom A),c)) . c9 is Element of the carrier of (Ens (Hom A))
Obj (hom?- ((Hom A),c)) is non empty Relation-like the carrier of A -defined the carrier of (Ens (Hom A)) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (Ens (Hom A))))
(Obj (hom?- ((Hom A),c))) . c9 is Element of the carrier of (Ens (Hom A))
Hom (((A,c9) . c9),((A,c) . c9)) is Element of K32( the carrier' of (A))
K32( the carrier' of (A)) is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,c9) . c9 & cod b<sub>1</sub> = (A,c) . c9 ) } is set
t is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,c9),(A,c)
t . c9 is Morphism of (A,c9) . c9,(A,c) . c9
cod (t . c9) is Element of the carrier of (A)
the Target of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
K33( the carrier' of (A), the carrier of (A)) is Relation-like set
K32(K33( the carrier' of (A), the carrier of (A))) is set
the Target of (A) . (t . c9) is Element of the carrier of (A)
fDom (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
K33((Maps (Hom A)),(Hom A)) is Relation-like set
K32(K33((Maps (Hom A)),(Hom A))) is set
fCod (Hom A) is non empty Relation-like Maps (Hom A) -defined Hom A -valued Function-like V17( Maps (Hom A)) quasi_total Element of K32(K33((Maps (Hom A)),(Hom A)))
fComp (Hom A) is Relation-like K33((Maps (Hom A)),(Maps (Hom A))) -defined Maps (Hom A) -valued Function-like Element of K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))))
K33((Maps (Hom A)),(Maps (Hom A))) is Relation-like set
K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A))) is Relation-like set
K32(K33(K33((Maps (Hom A)),(Maps (Hom A))),(Maps (Hom A)))) is set
CatStr(# (Hom A),(Maps (Hom A)),(fDom (Hom A)),(fCod (Hom A)),(fComp (Hom A)) #) is strict CatStr
(fCod (Hom A)) . (t . c9) is set
t1 is Element of Maps (Hom A)
cod t1 is Element of Hom A
dom t1 is Element of Hom A
Maps ((dom t1),(cod t1)) is set
t1 `2 is Relation-like Function-like set
Funcs ((dom t1),(cod t1)) is functional set
dom (t . c9) is Element of the carrier of (A)
the Source of (A) is non empty Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like V17( the carrier' of (A)) quasi_total Element of K32(K33( the carrier' of (A), the carrier of (A)))
the Source of (A) . (t . c9) is Element of the carrier of (A)
(fDom (Hom A)) . (t . c9) is set
K33(((A,c9) . c9),((A,c) . c9)) is Relation-like set
K32(K33(((A,c9) . c9),((A,c) . c9))) is set
proj1 (t1 `2) is set
(t1 `2) . (id c9) is set
proj2 (t1 `2) is set
f is Morphism of c,c9
dom f is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
K33( the carrier' of A, the carrier of A) is Relation-like set
K32(K33( the carrier' of A, the carrier of A)) is set
the Source of A . f is Element of the carrier of A
(A) . f is Element of the carrier' of (Functors (A,(A)))
cod f is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A, the carrier of A))
the Target of A . f is Element of the carrier of A
(A,(cod f)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (cod f) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
(A,(dom f)) is non empty Relation-like the carrier' of A -defined the carrier' of (A) -valued Function-like V17( the carrier' of A) quasi_total Functor of A,(A)
hom?- (dom f) is non empty Relation-like the carrier' of A -defined Maps (Hom A) -valued Function-like V17( the carrier' of A) quasi_total Element of K32(K33( the carrier' of A,(Maps (Hom A))))
(A,f) is non empty Relation-like the carrier of A -defined the carrier' of (A) -valued Function-like V17( the carrier of A) quasi_total natural_transformation of (A,(cod f)),(A,(dom f))
a is Element of the carrier of A
(A,f) . a is Morphism of (A,(cod f)) . a,(A,(dom f)) . a
(A,(cod f)) . a is Element of the carrier of (A)
Obj (A,(cod f)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(cod f))) . a is Element of the carrier of (A)
(A,(dom f)) . a is Element of the carrier of (A)
Obj (A,(dom f)) is non empty Relation-like the carrier of A -defined the carrier of (A) -valued Function-like V17( the carrier of A) quasi_total Element of K32(K33( the carrier of A, the carrier of (A)))
(Obj (A,(dom f))) . a is Element of the carrier of (A)
t . a is Morphism of (A,c9) . a,(A,c) . a
(A,c9) . a is Element of the carrier of (A)
(Obj (A,c9)) . a is Element of the carrier of (A)
(A,c) . a is Element of the carrier of (A)
(Obj (A,c)) . a is Element of the carrier of (A)
(hom?- ((Hom A),c)) . a is Element of the carrier of (Ens (Hom A))
(Obj (hom?- ((Hom A),c))) . a is Element of the carrier of (Ens (Hom A))
Hom (c,a) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c & cod b<sub>1</sub> = a ) } is set
(hom?- ((Hom A),c9)) . a is Element of the carrier of (Ens (Hom A))
(Obj (hom?- ((Hom A),c9))) . a is Element of the carrier of (Ens (Hom A))
Hom (c9,a) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c9 & cod b<sub>1</sub> = a ) } is set
ta1 is Element of Maps (Hom A)
dom ta1 is Element of Hom A
cod ta1 is Element of Hom A
Maps ((dom ta1),(cod ta1)) is set
ta1 `2 is Relation-like Function-like set
Funcs ((dom ta1),(cod ta1)) is functional set
K33((dom ta1),(cod ta1)) is Relation-like set
K32(K33((dom ta1),(cod ta1))) is set
proj1 (ta1 `2) is set
dom (t . a) is Element of the carrier of (A)
the Source of (A) . (t . a) is Element of the carrier of (A)
(fDom (Hom A)) . (t . a) is set
Hom (((A,c9) . a),((A,c) . a)) is Element of K32( the carrier' of (A))
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,c9) . a & cod b<sub>1</sub> = (A,c) . a ) } is set
cod (t . a) is Element of the carrier of (A)
the Target of (A) . (t . a) is Element of the carrier of (A)
(fCod (Hom A)) . (t . a) is set
[((A,c9) . a),((A,c) . a)] is V1() Element of the carrier of K210((A),(A))
K210((A),(A)) is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of K210((A),(A)) is non empty set
{((A,c9) . a),((A,c) . a)} is non empty set
{((A,c9) . a)} is non empty set
{{((A,c9) . a),((A,c) . a)},{((A,c9) . a)}} is non empty set
[[((A,c9) . a),((A,c) . a)],(ta1 `2)] is V1() set
{[((A,c9) . a),((A,c) . a)],(ta1 `2)} is non empty set
{[((A,c9) . a),((A,c) . a)]} is non empty Relation-like Function-like set
{{[((A,c9) . a),((A,c) . a)],(ta1 `2)},{[((A,c9) . a),((A,c) . a)]}} is non empty set
K33((dom (t . a)),(cod (t . a))) is Relation-like set
K32(K33((dom (t . a)),(cod (t . a)))) is set
Hom ((dom f),a) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom f & cod b₁ = a ) } is set
id a is Morphism of a,a
hom (f,(id a)) is Relation-like Hom ((cod f),(dom (id a))) -defined Hom ((dom f),(cod (id a))) -valued Function-like quasi_total Element of K32(K33((Hom ((cod f),(dom (id a)))),(Hom ((dom f),(cod (id a))))))
dom (id a) is Element of the carrier of A
the Source of A . (id a) is Element of the carrier of A
Hom ((cod f),(dom (id a))) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod f & cod b₁ = dom (id a) ) } is set
cod (id a) is Element of the carrier of A
the Target of A . (id a) is Element of the carrier of A
Hom ((dom f),(cod (id a))) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom f & cod b₁ = cod (id a) ) } is set
K33((Hom ((cod f),(dom (id a)))),(Hom ((dom f),(cod (id a))))) is Relation-like set
K32(K33((Hom ((cod f),(dom (id a)))),(Hom ((dom f),(cod (id a)))))) is set
x is set
(hom (f,(id a))) . x is set
(ta1 `2) . x is set
Hom (c,(cod f)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c & cod b<sub>1</sub> = cod f ) } is set
y is Morphism of cod f,a
h is Morphism of c9,a
dom h is Element of the carrier of A
the Source of A . h is Element of the carrier of A
(A,c9) . h is Element of the carrier' of (A)
cod h is Element of the carrier of A
the Target of A . h is Element of the carrier of A
(A,c) . h is Element of the carrier' of (A)
Hom (c,(dom h)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c & cod b<sub>1</sub> = dom h ) } is set
Hom (c,(cod h)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c & cod b<sub>1</sub> = cod h ) } is set
[(Hom (c,(dom h))),(Hom (c,(cod h)))] is V1() set
{(Hom (c,(dom h))),(Hom (c,(cod h)))} is non empty set
{(Hom (c,(dom h)))} is non empty set
{{(Hom (c,(dom h))),(Hom (c,(cod h)))},{(Hom (c,(dom h)))}} is non empty set
hom (c,h) is Relation-like Hom (c,(dom h)) -defined Hom (c,(cod h)) -valued Function-like quasi_total Element of K32(K33((Hom (c,(dom h))),(Hom (c,(cod h)))))
K33((Hom (c,(dom h))),(Hom (c,(cod h)))) is Relation-like set
K32(K33((Hom (c,(dom h))),(Hom (c,(cod h))))) is set
[[(Hom (c,(dom h))),(Hom (c,(cod h)))],(hom (c,h))] is V1() set
{[(Hom (c,(dom h))),(Hom (c,(cod h)))],(hom (c,h))} is non empty set
{[(Hom (c,(dom h))),(Hom (c,(cod h)))]} is non empty Relation-like Function-like set
{{[(Hom (c,(dom h))),(Hom (c,(cod h)))],(hom (c,h))},{[(Hom (c,(dom h))),(Hom (c,(cod h)))]}} is non empty set
(A,c) . h is set
Hom (c9,(dom h)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c9 & cod b<sub>1</sub> = dom h ) } is set
Hom (c9,(cod h)) is Element of K32( the carrier' of A)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of A : ( dom b<sub>1</sub> = c9 & cod b<sub>1</sub> = cod h ) } is set
[(Hom (c9,(dom h))),(Hom (c9,(cod h)))] is V1() set
{(Hom (c9,(dom h))),(Hom (c9,(cod h)))} is non empty set
{(Hom (c9,(dom h)))} is non empty set
{{(Hom (c9,(dom h))),(Hom (c9,(cod h)))},{(Hom (c9,(dom h)))}} is non empty set
hom (c9,h) is Relation-like Hom (c9,(dom h)) -defined Hom (c9,(cod h)) -valued Function-like quasi_total Element of K32(K33((Hom (c9,(dom h))),(Hom (c9,(cod h)))))
K33((Hom (c9,(dom h))),(Hom (c9,(cod h)))) is Relation-like set
K32(K33((Hom (c9,(dom h))),(Hom (c9,(cod h))))) is set
[[(Hom (c9,(dom h))),(Hom (c9,(cod h)))],(hom (c9,h))] is V1() set
{[(Hom (c9,(dom h))),(Hom (c9,(cod h)))],(hom (c9,h))} is non empty set
{[(Hom (c9,(dom h))),(Hom (c9,(cod h)))]} is non empty Relation-like Function-like set
{{[(Hom (c9,(dom h))),(Hom (c9,(cod h)))],(hom (c9,h))},{[(Hom (c9,(dom h))),(Hom (c9,(cod h)))]}} is non empty set
(A,c9) . h is set
cod ((A,c9) . h) is Element of the carrier of (A)
the Target of (A) . ((A,c9) . h) is Element of the carrier of (A)
(fCod (Hom A)) . ((A,c9) . h) is set
tc9 is Element of Maps (Hom A)
cod tc9 is Element of Hom A
tc9 `1 is set
(tc9 `1) `2 is set
[(Hom (c9,(dom h))),(Hom (c9,(cod h)))] `2 is set
[(t . a),((A,c9) . h)] is V1() Element of the carrier' of K210((A),(A))
the carrier' of K210((A),(A)) is non empty set
{(t . a),((A,c9) . h)} is non empty set
{(t . a)} is non empty set
{{(t . a),((A,c9) . h)},{(t . a)}} is non empty set
the Comp of (A) is Relation-like K33( the carrier' of (A), the carrier' of (A)) -defined the carrier' of (A) -valued Function-like Element of K32(K33(K33( the carrier' of (A), the carrier' of (A)), the carrier' of (A)))
K33( the carrier' of (A), the carrier' of (A)) is Relation-like set
K33(K33( the carrier' of (A), the carrier' of (A)), the carrier' of (A)) is Relation-like set
K32(K33(K33( the carrier' of (A), the carrier' of (A)), the carrier' of (A))) is set
proj1 the Comp of (A) is Relation-like set
dom tc9 is Element of Hom A
Maps ((dom tc9),(cod tc9)) is set
tc9 `2 is Relation-like Function-like set
Funcs ((dom tc9),(cod tc9)) is functional set
dom ((A,c9) . h) is Element of the carrier of (A)
the Source of (A) . ((A,c9) . h) is Element of the carrier of (A)
(fDom (Hom A)) . ((A,c9) . h) is set
(tc9 `1) `1 is set
[(Hom (c9,(dom h))),(Hom (c9,(cod h)))] `1 is set
proj1 (tc9 `2) is set
dom y is Element of the carrier of A
the Source of A . y is Element of the carrier of A
tch is Element of Maps (Hom A)
dom tch is Element of Hom A
cod tch is Element of Hom A
[(dom tch),(cod tch)] is V1() set
{(dom tch),(cod tch)} is non empty set
{(dom tch)} is non empty set
{{(dom tch),(cod tch)},{(dom tch)}} is non empty set
tch `2 is Relation-like Function-like set
[[(dom tch),(cod tch)],(tch `2)] is V1() set
{[(dom tch),(cod tch)],(tch `2)} is non empty set
{[(dom tch),(cod tch)]} is non empty Relation-like Function-like set
{{[(dom tch),(cod tch)],(tch `2)},{[(dom tch),(cod tch)]}} is non empty set
[(Hom (c,(dom h))),(Hom (c,(cod h))),(hom (c,h))] is V1() V2() set
[(dom tch),(cod tch),(tch `2)] is V1() V2() set
[(dom tc9),(cod tc9)] is V1() set
{(dom tc9),(cod tc9)} is non empty set
{(dom tc9)} is non empty set
{{(dom tc9),(cod tc9)},{(dom tc9)}} is non empty set
[[(dom tc9),(cod tc9)],(tc9 `2)] is V1() set
{[(dom tc9),(cod tc9)],(tc9 `2)} is non empty set
{[(dom tc9),(cod tc9)]} is non empty Relation-like Function-like set
{{[(dom tc9),(cod tc9)],(tc9 `2)},{[(dom tc9),(cod tc9)]}} is non empty set
[(dom tc9),(cod tc9),(tc9 `2)] is V1() V2() set
[(Hom (c9,(dom h))),(Hom (c9,(cod h))),(hom (c9,h))] is V1() V2() set
dom ((A,c) . h) is Element of the carrier of (A)
the Source of (A) . ((A,c) . h) is Element of the carrier of (A)
(fDom (Hom A)) . ((A,c) . h) is set
tch `1 is set
(tch `1) `1 is set
[(Hom (c,(dom h))),(Hom (c,(cod h)))] `1 is set
[((A,c) . h),(t . c9)] is V1() Element of the carrier' of K210((A),(A))
{((A,c) . h),(t . c9)} is non empty set
{((A,c) . h)} is non empty set
{{((A,c) . h),(t . c9)},{((A,c) . h)}} is non empty set
t1 is Element of Maps (Hom A)
cod t1 is Element of Hom A
(A,c) /. h is Morphism of (A,c) . c9,(A,c) . a
Hom (((A,c) . c9),((A,c) . a)) is Element of K32( the carrier' of (A))
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A) : ( dom b<sub>1</sub> = (A,c) . c9 & cod b<sub>1</sub> = (A,c) . a ) } is set
((A,c) /. h) * (t . c9) is Morphism of (A,c9) . c9,(A,c) . a
((A,c) . h) (*) (t . c9) is Element of the carrier' of (A)
(fComp (Hom A)) . (tch,t1) is set
[tch,t1] is V1() set
{tch,t1} is non empty set
{tch} is non empty set
{{tch,t1},{tch}} is non empty set
(fComp (Hom A)) . [tch,t1] is set
tch * t1 is Element of Maps (Hom A)
dom t1 is Element of Hom A
[(dom t1),(cod tch)] is V1() set
{(dom t1),(cod tch)} is non empty set
{(dom t1)} is non empty set
{{(dom t1),(cod tch)},{(dom t1)}} is non empty set
t1 `2 is Relation-like Function-like set
(t1 `2) * (tch `2) is Relation-like Function-like set
[[(dom t1),(cod tch)],((t1 `2) * (tch `2))] is V1() set
{[(dom t1),(cod tch)],((t1 `2) * (tch `2))} is non empty set
{[(dom t1),(cod tch)]} is non empty Relation-like Function-like set
{{[(dom t1),(cod tch)],((t1 `2) * (tch `2))},{[(dom t1),(cod tch)]}} is non empty set
(A,c9) /. h is Morphism of (A,c9) . c9,(A,c9) . a
Hom (((A,c9) . c9),((A,c9) . a)) is Element of K32( the carrier' of (A))
{ b₁ where b₁ is Element of the carrier' of (A) : ( dom b₁ = (A,c9) . c9 & cod b₁ = (A,c9) . a ) } is set
(t . a) * ((A,c9) /. h) is Morphism of (A,c9) . c9,(A,c) . a
(t . a) (*) ((A,c9) . h) is Element of the carrier' of (A)
(fComp (Hom A)) . (ta1,tc9) is set
[ta1,tc9] is V1() set
{ta1,tc9} is non empty set
{ta1} is non empty set
{{ta1,tc9},{ta1}} is non empty set
(fComp (Hom A)) . [ta1,tc9] is set
ta1 * tc9 is Element of Maps (Hom A)
[(dom tc9),(cod ta1)] is V1() set
{(dom tc9),(cod ta1)} is non empty set
{{(dom tc9),(cod ta1)},{(dom tc9)}} is non empty set
(tc9 `2) * (ta1 `2) is Relation-like Function-like set
[[(dom tc9),(cod ta1)],((tc9 `2) * (ta1 `2))] is V1() set
{[(dom tc9),(cod ta1)],((tc9 `2) * (ta1 `2))} is non empty set
{[(dom tc9),(cod ta1)]} is non empty Relation-like Function-like set
{{[(dom tc9),(cod ta1)],((tc9 `2) * (ta1 `2))},{[(dom tc9),(cod ta1)]}} is non empty set
[(dom tc9),(cod ta1),((tc9 `2) * (ta1 `2))] is V1() V2() set
[(dom t1),(cod tch),((t1 `2) * (tch `2))] is V1() V2() set
Hom (c9,(cod f)) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = c9 & cod b₁ = cod f ) } is set
hom (f,a) is Relation-like Hom ((cod f),a) -defined Hom ((dom f),a) -valued Function-like quasi_total Element of K32(K33((Hom ((cod f),a)),(Hom ((dom f),a))))
Hom ((cod f),a) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod f & cod b₁ = a ) } is set
Hom ((dom f),a) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom f & cod b₁ = a ) } is set
K33((Hom ((cod f),a)),(Hom ((dom f),a))) is Relation-like set
K32(K33((Hom ((cod f),a)),(Hom ((dom f),a)))) is set
(hom (f,a)) . y is set
y (*) f is Element of the carrier' of A
(t1 `2) . (id c9) is set
(tch `2) . ((t1 `2) . (id c9)) is set
((tc9 `2) * (ta1 `2)) . (id c9) is set
(hom (c9,h)) . (id c9) is set
(ta1 `2) . ((hom (c9,h)) . (id c9)) is set
y (*) (id c9) is Element of the carrier' of A
(ta1 `2) . (y (*) (id c9)) is set
hom (f,a) is Relation-like Hom ((cod f),a) -defined Hom ((dom f),a) -valued Function-like quasi_total Element of K32(K33((Hom ((cod f),a)),(Hom ((dom f),a))))
Hom ((cod f),a) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod f & cod b₁ = a ) } is set
Hom ((dom f),a) is Element of K32( the carrier' of A)
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom f & cod b₁ = a ) } is set
K33((Hom ((cod f),a)),(Hom ((dom f),a))) is Relation-like set
K32(K33((Hom ((cod f),a)),(Hom ((dom f),a)))) is set
proj1 (hom (f,a)) is set
proj1 (hom (f,(id a))) is set