:: ALTCAT_4 semantic presentation

K154() is M2( bool K150())
K150() is set
bool K150() is non empty set
K116() is set
bool K116() is non empty set
bool K154() is non empty set
{} is set
the Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty V36() V37() set is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty V36() V37() set
1 is non empty set
{{},1} is set
C is non empty with_units reflexive AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
<^i,i^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (i,i) is set
[i,i] is V15() set
{i,i} is set
{i} is set
{{i,i},{i}} is set
the Arrows of C . [i,i] is set
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
o1 is M2( the carrier of C)
<^i,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{i} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
idm o1 is M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
o2 is M2( the carrier of C)
<^i,o2^> is set
the Arrows of C . (i,o2) is set
[i,o2] is V15() set
{i,o2} is set
{{i,o2},{i}} is set
the Arrows of C . [i,o2] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
o1 is M2(<^i,o1^>)
o2 is M2(<^i,o2^>)
p1 is M2(<^o1,o2^>)
p1 * o1 is M2(<^i,o2^>)
p1 " is M2(<^o2,o1^>)
(p1 ") * p1 is M2(<^o1,o1^>)
(p1 ") * o2 is M2(<^i,o1^>)
((p1 ") * p1) * o1 is M2(<^i,o1^>)
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
idm i is M2(<^i,i^>)
<^i,i^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (i,i) is set
[i,i] is V15() set
{i,i} is set
{i} is set
{{i,i},{i}} is set
the Arrows of C . [i,i] is set
o1 is M2( the carrier of C)
<^i,o1^> is set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
o2 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o2,i^> is set
the Arrows of C . (o2,i) is set
[o2,i] is V15() set
{o2,i} is set
{{o2,i},{o2}} is set
the Arrows of C . [o2,i] is set
<^i,o2^> is set
the Arrows of C . (i,o2) is set
[i,o2] is V15() set
{i,o2} is set
{{i,o2},{i}} is set
the Arrows of C . [i,o2] is set
o1 is M2(<^i,o1^>)
o2 is M2(<^o2,o1^>)
p1 is M2(<^o2,i^>)
o1 * p1 is M2(<^o2,o1^>)
p1 " is M2(<^i,o2^>)
p1 * (p1 ") is M2(<^i,i^>)
o2 * (p1 ") is M2(<^i,o1^>)
o1 * (p1 * (p1 ")) is M2(<^i,o1^>)
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
o1 is M2( the carrier of C)
<^i,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{i} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
<^o1,i^> is set
the Arrows of C . (o1,i) is set
[o1,i] is V15() set
{o1,i} is set
{o1} is set
{{o1,i},{o1}} is set
the Arrows of C . [o1,i] is set
o2 is M2(<^i,o1^>)
o2 " is M2(<^o1,i^>)
(o2 ") " is M2(<^i,o1^>)
(o2 ") * ((o2 ") ") is M2(<^i,i^>)
<^i,i^> is non empty set
the Arrows of C . (i,i) is set
[i,i] is V15() set
{i,i} is set
{{i,i},{i}} is set
the Arrows of C . [i,i] is set
(o2 ") * o2 is M2(<^i,i^>)
idm i is M2(<^i,i^>)
((o2 ") ") * (o2 ") is M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
idm o1 is M2(<^o1,o1^>)
o2 * (o2 ") is M2(<^o1,o1^>)
C is non empty with_units reflexive AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
idm i is M2(<^i,i^>)
<^i,i^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (i,i) is set
[i,i] is V15() set
{i,i} is set
{i} is set
{{i,i},{i}} is set
the Arrows of C . [i,i] is set
o1 is M2( the carrier of C)
<^i,o1^> is set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
o2 is M2(<^i,o1^>)
o2 * (idm i) is M2(<^i,o1^>)
o1 is M2(<^i,o1^>)
o1 * (idm i) is M2(<^i,o1^>)
o1 is M2( the carrier of C)
<^o1,i^> is set
the Arrows of C . (o1,i) is set
[o1,i] is V15() set
{o1,i} is set
{o1} is set
{{o1,i},{o1}} is set
the Arrows of C . [o1,i] is set
o2 is M2(<^o1,i^>)
(idm i) * o2 is M2(<^o1,i^>)
o1 is M2(<^o1,i^>)
(idm i) * o1 is M2(<^o1,i^>)
C is non empty with_units reflexive AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
idm i is M2(<^i,i^>)
<^i,i^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (i,i) is set
[i,i] is V15() set
{i,i} is set
{i} is set
{{i,i},{i}} is set
the Arrows of C . [i,i] is set
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
idm i is retraction coretraction mono epi M2(<^i,i^>)
<^i,i^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (i,i) is set
[i,i] is V15() set
{i,i} is set
{i} is set
{{i,i},{i}} is set
the Arrows of C . [i,i] is set
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
idm i is retraction coretraction iso mono epi M2(<^i,i^>)
<^i,i^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (i,i) is set
[i,i] is V15() set
{i,i} is set
{i} is set
{{i,i},{i}} is set
the Arrows of C . [i,i] is set
o1 is M2( the carrier of C)
<^i,o1^> is set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
<^o1,i^> is set
the Arrows of C . (o1,i) is set
[o1,i] is V15() set
{o1,i} is set
{o1} is set
{{o1,i},{o1}} is set
the Arrows of C . [o1,i] is set
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
o2 is M2(<^i,o1^>)
o2 is M2(<^o1,i^>)
o2 * o2 is M2(<^i,i^>)
o1 is M2(<^o1,i^>)
o2 * o1 is M2(<^o1,o1^>)
(o2 * o2) * o1 is M2(<^o1,i^>)
o2 * (idm o1) is M2(<^o1,i^>)
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
o1 is M2( the carrier of C)
<^i,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{i} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
<^o1,i^> is set
the Arrows of C . (o1,i) is set
[o1,i] is V15() set
{o1,i} is set
{o1} is set
{{o1,i},{o1}} is set
the Arrows of C . [o1,i] is set
o2 is M2(<^i,o1^>)
o1 is M2(<^o1,i^>)
o2 * o1 is M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
o1 * (o2 * o1) is M2(<^o1,i^>)
o1 * o2 is M2(<^i,i^>)
<^i,i^> is non empty set
the Arrows of C . (i,i) is set
[i,i] is V15() set
{i,i} is set
{{i,i},{i}} is set
the Arrows of C . [i,i] is set
(o1 * o2) * o1 is M2(<^o1,i^>)
idm i is retraction coretraction iso mono epi M2(<^i,i^>)
(idm i) * o1 is M2(<^o1,i^>)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
o1 * (idm o1) is M2(<^o1,i^>)
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
o1 is M2( the carrier of C)
<^i,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{i} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
o2 is M2(<^i,o1^>)
o1 is M2(<^i,o1^>)
o2 is M2( the carrier of C)
<^o2,o2^> is non empty set
the Arrows of C . (o2,o2) is set
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the Arrows of C . [o2,o2] is set
the M2(<^o2,o2^>) is M2(<^o2,o2^>)
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
the M2(<^o2,o1^>) is M2(<^o2,o1^>)
<^i,o2^> is set
the Arrows of C . (i,o2) is set
[i,o2] is V15() set
{i,o2} is set
{{i,o2},{i}} is set
the Arrows of C . [i,o2] is set
the M2(<^i,o2^>) is M2(<^i,o2^>)
the M2(<^o2,o2^>) " is M2(<^o2,o2^>)
( the M2(<^o2,o2^>) ") * the M2(<^o2,o2^>) is M2(<^o2,o2^>)
the M2(<^o2,o1^>) * (( the M2(<^o2,o2^>) ") * the M2(<^o2,o2^>)) is M2(<^o2,o1^>)
( the M2(<^o2,o1^>) * (( the M2(<^o2,o2^>) ") * the M2(<^o2,o2^>))) * the M2(<^i,o2^>) is M2(<^i,o1^>)
C is non empty AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
o1 is M2( the carrier of C)
<^i,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{i} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
o2 is M2(<^i,o1^>)
o1 is M2( the carrier of C)
<^o1,i^> is set
the Arrows of C . (o1,i) is set
[o1,i] is V15() set
{o1,i} is set
{o1} is set
{{o1,i},{o1}} is set
the Arrows of C . [o1,i] is set
o2 is M2(<^o1,i^>)
o2 * o2 is M2(<^o1,o1^>)
<^o1,o1^> is set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
p1 is M2(<^o1,i^>)
o2 * p1 is M2(<^o1,o1^>)
p2 is M2(<^o1,i^>)
C is non empty AltCatStr
the carrier of C is non empty set
o1 is M2( the carrier of C)
i is M2( the carrier of C)
<^o1,i^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,i) is set
[o1,i] is V15() set
{o1,i} is set
{o1} is set
{{o1,i},{o1}} is set
the Arrows of C . [o1,i] is set
o2 is M2(<^o1,i^>)
o1 is M2( the carrier of C)
<^i,o1^> is set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{i} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
o2 is M2(<^i,o1^>)
o2 * o2 is M2(<^o1,o1^>)
<^o1,o1^> is set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
p1 is M2(<^i,o1^>)
p1 * o2 is M2(<^o1,o1^>)
p2 is M2(<^i,o1^>)
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o1,i^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,i) is set
[o1,i] is V15() set
{o1,i} is set
{o1} is set
{{o1,i},{o1}} is set
the Arrows of C . [o1,i] is set
o2 is M2(<^o1,i^>)
o2 " is M2(<^i,o1^>)
<^i,o1^> is set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{i} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
(o2 ") * o2 is M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
o1 is M2( the carrier of C)
<^o1,o1^> is set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
<^o1,i^> is set
the Arrows of C . (o1,i) is set
[o1,i] is V15() set
{o1,i} is set
{{o1,i},{o1}} is set
the Arrows of C . [o1,i] is set
o2 is M2(<^o1,i^>)
(o2 ") * o2 is M2(<^o1,o1^>)
p1 is M2(<^o1,o1^>)
o2 * p1 is M2(<^o1,i^>)
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
o1 is M2( the carrier of C)
<^i,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{i} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
o2 is M2(<^i,o1^>)
o2 " is M2(<^o1,i^>)
<^o1,i^> is set
the Arrows of C . (o1,i) is set
[o1,i] is V15() set
{o1,i} is set
{o1} is set
{{o1,i},{o1}} is set
the Arrows of C . [o1,i] is set
o2 * (o2 ") is M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
o1 is M2( the carrier of C)
<^o1,o1^> is set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
<^i,o1^> is set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
o2 is M2(<^i,o1^>)
o2 * (o2 ") is M2(<^o1,o1^>)
p1 is M2(<^o1,o1^>)
p1 * o2 is M2(<^i,o1^>)
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
i is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o1,i^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,i) is set
[o1,i] is V15() set
{o1,i} is set
{o1} is set
{{o1,i},{o1}} is set
the Arrows of C . [o1,i] is set
<^i,o1^> is set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{i} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
o2 is M2(<^i,o1^>)
o1 is set
p1 is M2( the carrier of C)
<^o1,p1^> is set
the Arrows of C . (o1,p1) is set
[o1,p1] is V15() set
{o1,p1} is set
{{o1,p1},{o1}} is set
the Arrows of C . [o1,p1] is set
<^i,p1^> is set
the Arrows of C . (i,p1) is set
[i,p1] is V15() set
{i,p1} is set
{{i,p1},{i}} is set
the Arrows of C . [i,p1] is set
p2 is M2(<^i,p1^>)
o2 is M2(<^o1,i^>)
p2 * o2 is M2(<^o1,p1^>)
n is M2(<^o1,p1^>)
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
n2 is M2(<^o1,o1^>)
n * o2 is M2(<^i,p1^>)
(n * o2) * o2 is M2(<^o1,p1^>)
o2 * o2 is M2(<^o1,o1^>)
n * (o2 * o2) is M2(<^o1,p1^>)
n * n2 is M2(<^o1,p1^>)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
n * (idm o1) is M2(<^o1,p1^>)
p1 is M2( the carrier of C)
<^p1,i^> is set
the Arrows of C . (p1,i) is set
[p1,i] is V15() set
{p1,i} is set
{p1} is set
{{p1,i},{p1}} is set
the Arrows of C . [p1,i] is set
<^p1,o1^> is set
the Arrows of C . (p1,o1) is set
[p1,o1] is V15() set
{p1,o1} is set
{{p1,o1},{p1}} is set
the Arrows of C . [p1,o1] is set
p2 is M2(<^p1,o1^>)
o2 is M2(<^o1,i^>)
o2 * p2 is M2(<^p1,i^>)
n is M2(<^p1,i^>)
<^i,i^> is non empty set
the Arrows of C . (i,i) is set
[i,i] is V15() set
{i,i} is set
{{i,i},{i}} is set
the Arrows of C . [i,i] is set
n2 is M2(<^i,i^>)
o2 * n is M2(<^p1,o1^>)
o2 * (o2 * n) is M2(<^p1,i^>)
o2 * o2 is M2(<^i,i^>)
(o2 * o2) * n is M2(<^p1,i^>)
n2 * n is M2(<^p1,i^>)
idm i is retraction coretraction iso mono epi M2(<^i,i^>)
(idm i) * n is M2(<^p1,i^>)
C is non empty transitive with_units reflexive AltCatStr
i is non empty transitive with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of C,i
o2 is M2( the carrier of C)
idm o2 is retraction coretraction mono epi M2(<^o2,o2^>)
<^o2,o2^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o2) is set
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the Arrows of C . [o2,o2] is set
o1 . (idm o2) is M2(<^(o1 . o2),(o1 . o2)^>)
o1 . o2 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
<^(o1 . o2),(o1 . o2)^> is non empty set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o2),(o1 . o2)) is set
[(o1 . o2),(o1 . o2)] is V15() set
{(o1 . o2),(o1 . o2)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o2)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o2)] is set
idm (o1 . o2) is retraction coretraction mono epi M2(<^(o1 . o2),(o1 . o2)^>)
Morph-Map (o1,o2,o2) is Relation-like <^o2,o2^> -defined <^(o1 . o2),(o1 . o2)^> -valued Function-like quasi_total M2( bool [:<^o2,o2^>,<^(o1 . o2),(o1 . o2)^>:])
[:<^o2,o2^>,<^(o1 . o2),(o1 . o2)^>:] is Relation-like non empty set
bool [:<^o2,o2^>,<^(o1 . o2),(o1 . o2)^>:] is non empty set
the MorphMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) V36() V37() MSUnTrans of the ObjectMap of o1, the Arrows of C, the Arrows of i
the MorphMap of o1 . (o2,o2) is set
the MorphMap of o1 . [o2,o2] is Relation-like Function-like set
(Morph-Map (o1,o2,o2)) . (idm o2) is M2(<^(o1 . o2),(o1 . o2)^>)
C is non empty AltCatStr
i is non empty AltCatStr
the carrier of C is non empty set
o1 is reflexive Contravariant FunctorStr over C,i
[: the carrier of C, the carrier of C:] is Relation-like non empty set
o1 is M2( the carrier of C)
o1 . o1 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o2 is M2( the carrier of C)
o1 . o2 is M2( the carrier of i)
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
Morph-Map (o1,o2,o1) is Relation-like <^o2,o1^> -defined <^(o1 . o1),(o1 . o2)^> -valued Function-like quasi_total M2( bool [:<^o2,o1^>,<^(o1 . o1),(o1 . o2)^>:])
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
[:<^o2,o1^>,<^(o1 . o1),(o1 . o2)^>:] is Relation-like set
bool [:<^o2,o1^>,<^(o1 . o1),(o1 . o2)^>:] is non empty set
the MorphMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) V36() V37() MSUnTrans of the ObjectMap of o1, the Arrows of C, the Arrows of i
the MorphMap of o1 . (o2,o1) is set
the MorphMap of o1 . [o2,o1] is Relation-like Function-like set
proj1 the ObjectMap of o1 is Relation-like set
the ObjectMap of o1 * the Arrows of i is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
p1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of the Arrows of C, the ObjectMap of o1 * the Arrows of i
p1 . [o2,o1] is Relation-like Function-like set
proj2 (p1 . [o2,o1]) is set
( the ObjectMap of o1 * the Arrows of i) . [o2,o1] is set
proj2 (Morph-Map (o1,o2,o1)) is set
the ObjectMap of o1 . (o2,o1) is M2([: the carrier of i, the carrier of i:])
the ObjectMap of o1 . [o2,o1] is set
the Arrows of i . ( the ObjectMap of o1 . (o2,o1)) is set
the ObjectMap of o1 * the Arrows of i is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
o2 is non empty set
[:[: the carrier of C, the carrier of C:],o2:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],o2:] is non empty set
p2 is Relation-like [: the carrier of C, the carrier of C:] -defined o2 -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],o2:])
p1 is Relation-like o2 -defined Function-like non empty V14(o2) set
p2 * p1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of the Arrows of C, the ObjectMap of o1 * the Arrows of i
o2 is set
o1 . o2 is Relation-like Function-like set
proj2 (o1 . o2) is set
( the ObjectMap of o1 * the Arrows of i) . o2 is set
p1 is set
p2 is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
n2 is M2( the carrier of C)
n is M2( the carrier of C)
[n2,n] is V15() set
{n2,n} is set
{n2} is set
{{n2,n},{n2}} is set
proj1 the ObjectMap of o1 is Relation-like set
o1 . n is M2( the carrier of i)
the ObjectMap of o1 . (n,n) is M2([: the carrier of i, the carrier of i:])
[n,n] is V15() set
{n,n} is set
{n} is set
{{n,n},{n}} is set
the ObjectMap of o1 . [n,n] is set
K40(( the ObjectMap of o1 . (n,n))) is set
o1 . n2 is M2( the carrier of i)
the ObjectMap of o1 . (n2,n2) is M2([: the carrier of i, the carrier of i:])
[n2,n2] is V15() set
{n2,n2} is set
{{n2,n2},{n2}} is set
the ObjectMap of o1 . [n2,n2] is set
K40(( the ObjectMap of o1 . (n2,n2))) is set
<^(o1 . n),(o1 . n2)^> is set
the Arrows of i . ((o1 . n),(o1 . n2)) is set
[(o1 . n),(o1 . n2)] is V15() set
{(o1 . n),(o1 . n2)} is set
{(o1 . n)} is set
{{(o1 . n),(o1 . n2)},{(o1 . n)}} is set
the Arrows of i . [(o1 . n),(o1 . n2)] is set
Morph-Map (o1,n2,n) is Relation-like <^n2,n^> -defined <^(o1 . n),(o1 . n2)^> -valued Function-like quasi_total M2( bool [:<^n2,n^>,<^(o1 . n),(o1 . n2)^>:])
<^n2,n^> is set
the Arrows of C . (n2,n) is set
the Arrows of C . [n2,n] is set
[:<^n2,n^>,<^(o1 . n),(o1 . n2)^>:] is Relation-like set
bool [:<^n2,n^>,<^(o1 . n),(o1 . n2)^>:] is non empty set
the MorphMap of o1 . (n2,n) is set
the MorphMap of o1 . [n2,n] is Relation-like Function-like set
proj2 (Morph-Map (o1,n2,n)) is set
the ObjectMap of o1 . (n2,n) is M2([: the carrier of i, the carrier of i:])
the ObjectMap of o1 . [n2,n] is set
the Arrows of i . ( the ObjectMap of o1 . (n2,n)) is set
( the ObjectMap of o1 * the Arrows of i) . [n2,n] is set
C is non empty AltCatStr
i is non empty AltCatStr
the carrier of C is non empty set
o1 is reflexive Contravariant FunctorStr over C,i
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the MorphMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) V36() V37() MSUnTrans of the ObjectMap of o1, the Arrows of C, the Arrows of i
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
proj1 the MorphMap of o1 is non empty set
Morph-Map (o1,o2,o1) is Relation-like <^o2,o1^> -defined <^(o1 . o1),(o1 . o2)^> -valued Function-like quasi_total M2( bool [:<^o2,o1^>,<^(o1 . o1),(o1 . o2)^>:])
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
the Arrows of C . [o2,o1] is set
o1 . o1 is M2( the carrier of i)
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o1 . o2 is M2( the carrier of i)
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
[:<^o2,o1^>,<^(o1 . o1),(o1 . o2)^>:] is Relation-like set
bool [:<^o2,o1^>,<^(o1 . o1),(o1 . o2)^>:] is non empty set
the MorphMap of o1 . (o2,o1) is set
the MorphMap of o1 . [o2,o1] is Relation-like Function-like set
o1 is set
the MorphMap of o1 . o1 is Relation-like Function-like set
o2 is Relation-like Function-like set
p1 is set
p2 is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
n is M2( the carrier of C)
n2 is M2( the carrier of C)
the MorphMap of o1 . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the MorphMap of o1 . [n,n2] is Relation-like Function-like set
Morph-Map (o1,n,n2) is Relation-like <^n,n2^> -defined <^(o1 . n2),(o1 . n)^> -valued Function-like quasi_total M2( bool [:<^n,n2^>,<^(o1 . n2),(o1 . n)^>:])
<^n,n2^> is set
the Arrows of C . (n,n2) is set
the Arrows of C . [n,n2] is set
o1 . n2 is M2( the carrier of i)
the ObjectMap of o1 . (n2,n2) is M2([: the carrier of i, the carrier of i:])
[n2,n2] is V15() set
{n2,n2} is set
{n2} is set
{{n2,n2},{n2}} is set
the ObjectMap of o1 . [n2,n2] is set
K40(( the ObjectMap of o1 . (n2,n2))) is set
o1 . n is M2( the carrier of i)
the ObjectMap of o1 . (n,n) is M2([: the carrier of i, the carrier of i:])
[n,n] is V15() set
{n,n} is set
{{n,n},{n}} is set
the ObjectMap of o1 . [n,n] is set
K40(( the ObjectMap of o1 . (n,n))) is set
<^(o1 . n2),(o1 . n)^> is set
the Arrows of i . ((o1 . n2),(o1 . n)) is set
[(o1 . n2),(o1 . n)] is V15() set
{(o1 . n2),(o1 . n)} is set
{(o1 . n2)} is set
{{(o1 . n2),(o1 . n)},{(o1 . n2)}} is set
the Arrows of i . [(o1 . n2),(o1 . n)] is set
[:<^n,n2^>,<^(o1 . n2),(o1 . n)^>:] is Relation-like set
bool [:<^n,n2^>,<^(o1 . n2),(o1 . n)^>:] is non empty set
C is non empty AltCatStr
i is non empty AltCatStr
the carrier of C is non empty set
o1 is reflexive Covariant FunctorStr over C,i
o2 is M2( the carrier of C)
o1 . o2 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[: the carrier of C, the carrier of C:] is Relation-like non empty set
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o1 is M2( the carrier of C)
o1 . o1 is M2( the carrier of i)
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
o2 is M2(<^(o1 . o2),(o1 . o1)^>)
Morph-Map (o1,o2,o1) is Relation-like <^o2,o1^> -defined <^(o1 . o2),(o1 . o1)^> -valued Function-like quasi_total M2( bool [:<^o2,o1^>,<^(o1 . o2),(o1 . o1)^>:])
[:<^o2,o1^>,<^(o1 . o2),(o1 . o1)^>:] is Relation-like set
bool [:<^o2,o1^>,<^(o1 . o2),(o1 . o1)^>:] is non empty set
the MorphMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) V36() V37() MSUnTrans of the ObjectMap of o1, the Arrows of C, the Arrows of i
the MorphMap of o1 . (o2,o1) is set
the MorphMap of o1 . [o2,o1] is Relation-like Function-like set
proj2 (Morph-Map (o1,o2,o1)) is set
proj1 (Morph-Map (o1,o2,o1)) is set
p1 is set
(Morph-Map (o1,o2,o1)) . p1 is set
p2 is M2(<^o2,o1^>)
o1 . p2 is M2(<^(o1 . o2),(o1 . o1)^>)
C is non empty AltCatStr
i is non empty AltCatStr
the carrier of C is non empty set
o1 is reflexive Contravariant FunctorStr over C,i
o1 is M2( the carrier of C)
o1 . o1 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[: the carrier of C, the carrier of C:] is Relation-like non empty set
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o2 is M2( the carrier of C)
o1 . o2 is M2( the carrier of i)
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
o2 is M2(<^(o1 . o1),(o1 . o2)^>)
Morph-Map (o1,o2,o1) is Relation-like <^o2,o1^> -defined <^(o1 . o1),(o1 . o2)^> -valued Function-like quasi_total M2( bool [:<^o2,o1^>,<^(o1 . o1),(o1 . o2)^>:])
[:<^o2,o1^>,<^(o1 . o1),(o1 . o2)^>:] is Relation-like set
bool [:<^o2,o1^>,<^(o1 . o1),(o1 . o2)^>:] is non empty set
the MorphMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) V36() V37() MSUnTrans of the ObjectMap of o1, the Arrows of C, the Arrows of i
the MorphMap of o1 . (o2,o1) is set
the MorphMap of o1 . [o2,o1] is Relation-like Function-like set
proj2 (Morph-Map (o1,o2,o1)) is set
proj1 (Morph-Map (o1,o2,o1)) is set
p1 is set
(Morph-Map (o1,o2,o1)) . p1 is set
p2 is M2(<^o2,o1^>)
o1 . p2 is M2(<^(o1 . o1),(o1 . o2)^>)
C is non empty transitive with_units reflexive AltCatStr
i is non empty transitive with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o2 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o1 . o1 is M2( the carrier of i)
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o2 is M2(<^o2,o1^>)
o1 . o2 is M2(<^(o1 . o2),(o1 . o1)^>)
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
p1 is M2(<^o1,o2^>)
o1 . p1 is M2(<^(o1 . o1),(o1 . o2)^>)
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
o2 * p1 is M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
the Arrows of C . [o1,o1] is set
idm o1 is retraction coretraction mono epi M2(<^o1,o1^>)
(o1 . o2) * (o1 . p1) is M2(<^(o1 . o1),(o1 . o1)^>)
<^(o1 . o1),(o1 . o1)^> is non empty set
the Arrows of i . ((o1 . o1),(o1 . o1)) is set
[(o1 . o1),(o1 . o1)] is V15() set
{(o1 . o1),(o1 . o1)} is set
{{(o1 . o1),(o1 . o1)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o1)] is set
o1 . (idm o1) is M2(<^(o1 . o1),(o1 . o1)^>)
idm (o1 . o1) is retraction coretraction mono epi M2(<^(o1 . o1),(o1 . o1)^>)
C is non empty transitive with_units reflexive AltCatStr
i is non empty transitive with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o2 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o1 . o1 is M2( the carrier of i)
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o2 is M2(<^o2,o1^>)
o1 . o2 is M2(<^(o1 . o2),(o1 . o1)^>)
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
p1 is M2(<^o1,o2^>)
o1 . p1 is M2(<^(o1 . o1),(o1 . o2)^>)
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
p1 * o2 is M2(<^o2,o2^>)
<^o2,o2^> is non empty set
the Arrows of C . (o2,o2) is set
the Arrows of C . [o2,o2] is set
idm o2 is retraction coretraction mono epi M2(<^o2,o2^>)
(o1 . p1) * (o1 . o2) is M2(<^(o1 . o2),(o1 . o2)^>)
<^(o1 . o2),(o1 . o2)^> is non empty set
the Arrows of i . ((o1 . o2),(o1 . o2)) is set
[(o1 . o2),(o1 . o2)] is V15() set
{(o1 . o2),(o1 . o2)} is set
{{(o1 . o2),(o1 . o2)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o2)] is set
o1 . (idm o2) is M2(<^(o1 . o2),(o1 . o2)^>)
idm (o1 . o2) is retraction coretraction mono epi M2(<^(o1 . o2),(o1 . o2)^>)
C is non empty transitive V129() with_units reflexive AltCatStr
i is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o2 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o1 . o1 is M2( the carrier of i)
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o2 is M2(<^o2,o1^>)
o1 . o2 is M2(<^(o1 . o2),(o1 . o1)^>)
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
C is non empty transitive V129() with_units reflexive AltCatStr
i is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
o1 . o2 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[: the carrier of C, the carrier of C:] is Relation-like non empty set
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o1 . o1 is M2( the carrier of i)
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
o2 is M2(<^o2,o1^>)
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
o1 . o2 is M2(<^(o1 . o2),(o1 . o1)^>)
C is non empty transitive with_units reflexive AltCatStr
i is non empty transitive with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o1 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o1 . o2 is M2( the carrier of i)
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o2 is M2(<^o2,o1^>)
o1 . o2 is M2(<^(o1 . o1),(o1 . o2)^>)
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
p1 is M2(<^o1,o2^>)
o1 . p1 is M2(<^(o1 . o2),(o1 . o1)^>)
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
o2 * p1 is M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
the Arrows of C . [o1,o1] is set
idm o1 is retraction coretraction mono epi M2(<^o1,o1^>)
(o1 . p1) * (o1 . o2) is M2(<^(o1 . o1),(o1 . o1)^>)
<^(o1 . o1),(o1 . o1)^> is non empty set
the Arrows of i . ((o1 . o1),(o1 . o1)) is set
[(o1 . o1),(o1 . o1)] is V15() set
{(o1 . o1),(o1 . o1)} is set
{{(o1 . o1),(o1 . o1)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o1)] is set
o1 . (idm o1) is M2(<^(o1 . o1),(o1 . o1)^>)
idm (o1 . o1) is retraction coretraction mono epi M2(<^(o1 . o1),(o1 . o1)^>)
C is non empty transitive with_units reflexive AltCatStr
i is non empty transitive with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o1 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o1 . o2 is M2( the carrier of i)
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o2 is M2(<^o2,o1^>)
o1 . o2 is M2(<^(o1 . o1),(o1 . o2)^>)
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
p1 is M2(<^o1,o2^>)
o1 . p1 is M2(<^(o1 . o2),(o1 . o1)^>)
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
p1 * o2 is M2(<^o2,o2^>)
<^o2,o2^> is non empty set
the Arrows of C . (o2,o2) is set
the Arrows of C . [o2,o2] is set
idm o2 is retraction coretraction mono epi M2(<^o2,o2^>)
(o1 . o2) * (o1 . p1) is M2(<^(o1 . o2),(o1 . o2)^>)
<^(o1 . o2),(o1 . o2)^> is non empty set
the Arrows of i . ((o1 . o2),(o1 . o2)) is set
[(o1 . o2),(o1 . o2)] is V15() set
{(o1 . o2),(o1 . o2)} is set
{{(o1 . o2),(o1 . o2)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o2)] is set
o1 . (idm o2) is M2(<^(o1 . o2),(o1 . o2)^>)
idm (o1 . o2) is retraction coretraction mono epi M2(<^(o1 . o2),(o1 . o2)^>)
C is non empty transitive V129() with_units reflexive AltCatStr
i is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o1 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o1 . o2 is M2( the carrier of i)
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o2 is M2(<^o2,o1^>)
o1 . o2 is M2(<^(o1 . o1),(o1 . o2)^>)
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
C is non empty transitive V129() with_units reflexive AltCatStr
i is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
o1 . o1 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[: the carrier of C, the carrier of C:] is Relation-like non empty set
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o1 . o2 is M2( the carrier of i)
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
o2 is M2(<^o2,o1^>)
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
o1 . o2 is M2(<^(o1 . o1),(o1 . o2)^>)
C is non empty transitive with_units reflexive AltCatStr
i is non empty transitive with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o2 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o1 . o1 is M2( the carrier of i)
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o2 is M2(<^o2,o1^>)
o1 . o2 is M2(<^(o1 . o2),(o1 . o1)^>)
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
p1 is M2(<^(o1 . o1),(o1 . o2)^>)
Morph-Map (o1,o1,o2) is Relation-like <^o1,o2^> -defined <^(o1 . o1),(o1 . o2)^> -valued Function-like quasi_total M2( bool [:<^o1,o2^>,<^(o1 . o1),(o1 . o2)^>:])
[:<^o1,o2^>,<^(o1 . o1),(o1 . o2)^>:] is Relation-like set
bool [:<^o1,o2^>,<^(o1 . o1),(o1 . o2)^>:] is non empty set
the MorphMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) V36() V37() MSUnTrans of the ObjectMap of o1, the Arrows of C, the Arrows of i
the MorphMap of o1 . (o1,o2) is set
the MorphMap of o1 . [o1,o2] is Relation-like Function-like set
proj2 (Morph-Map (o1,o1,o2)) is set
proj1 (Morph-Map (o1,o1,o2)) is set
p2 is set
(Morph-Map (o1,o1,o2)) . p2 is set
n is M2(<^o1,o2^>)
(o1 . o2) * p1 is M2(<^(o1 . o1),(o1 . o1)^>)
<^(o1 . o1),(o1 . o1)^> is non empty set
the Arrows of i . ((o1 . o1),(o1 . o1)) is set
[(o1 . o1),(o1 . o1)] is V15() set
{(o1 . o1),(o1 . o1)} is set
{{(o1 . o1),(o1 . o1)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o1)] is set
idm (o1 . o1) is retraction coretraction mono epi M2(<^(o1 . o1),(o1 . o1)^>)
Morph-Map (o1,o1,o1) is Relation-like <^o1,o1^> -defined <^(o1 . o1),(o1 . o1)^> -valued Function-like quasi_total M2( bool [:<^o1,o1^>,<^(o1 . o1),(o1 . o1)^>:])
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
the Arrows of C . [o1,o1] is set
[:<^o1,o1^>,<^(o1 . o1),(o1 . o1)^>:] is Relation-like non empty set
bool [:<^o1,o1^>,<^(o1 . o1),(o1 . o1)^>:] is non empty set
the MorphMap of o1 . (o1,o1) is set
the MorphMap of o1 . [o1,o1] is Relation-like Function-like set
proj1 (Morph-Map (o1,o1,o1)) is set
idm o1 is retraction coretraction mono epi M2(<^o1,o1^>)
(Morph-Map (o1,o1,o1)) . (idm o1) is M2(<^(o1 . o1),(o1 . o1)^>)
o1 . (idm o1) is M2(<^(o1 . o1),(o1 . o1)^>)
o1 . n is M2(<^(o1 . o1),(o1 . o2)^>)
(o1 . o2) * (o1 . n) is M2(<^(o1 . o1),(o1 . o1)^>)
o2 * n is M2(<^o1,o1^>)
o1 . (o2 * n) is M2(<^(o1 . o1),(o1 . o1)^>)
(Morph-Map (o1,o1,o1)) . (o2 * n) is M2(<^(o1 . o1),(o1 . o1)^>)
C is non empty transitive with_units reflexive AltCatStr
i is non empty transitive with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o2 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o1 . o1 is M2( the carrier of i)
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o2 is M2(<^o2,o1^>)
o1 . o2 is M2(<^(o1 . o2),(o1 . o1)^>)
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
p1 is M2(<^(o1 . o1),(o1 . o2)^>)
Morph-Map (o1,o1,o2) is Relation-like <^o1,o2^> -defined <^(o1 . o1),(o1 . o2)^> -valued Function-like quasi_total M2( bool [:<^o1,o2^>,<^(o1 . o1),(o1 . o2)^>:])
[:<^o1,o2^>,<^(o1 . o1),(o1 . o2)^>:] is Relation-like set
bool [:<^o1,o2^>,<^(o1 . o1),(o1 . o2)^>:] is non empty set
the MorphMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) V36() V37() MSUnTrans of the ObjectMap of o1, the Arrows of C, the Arrows of i
the MorphMap of o1 . (o1,o2) is set
the MorphMap of o1 . [o1,o2] is Relation-like Function-like set
proj2 (Morph-Map (o1,o1,o2)) is set
proj1 (Morph-Map (o1,o1,o2)) is set
p2 is set
(Morph-Map (o1,o1,o2)) . p2 is set
n is M2(<^o1,o2^>)
p1 * (o1 . o2) is M2(<^(o1 . o2),(o1 . o2)^>)
<^(o1 . o2),(o1 . o2)^> is non empty set
the Arrows of i . ((o1 . o2),(o1 . o2)) is set
[(o1 . o2),(o1 . o2)] is V15() set
{(o1 . o2),(o1 . o2)} is set
{{(o1 . o2),(o1 . o2)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o2)] is set
idm (o1 . o2) is retraction coretraction mono epi M2(<^(o1 . o2),(o1 . o2)^>)
Morph-Map (o1,o2,o2) is Relation-like <^o2,o2^> -defined <^(o1 . o2),(o1 . o2)^> -valued Function-like quasi_total M2( bool [:<^o2,o2^>,<^(o1 . o2),(o1 . o2)^>:])
<^o2,o2^> is non empty set
the Arrows of C . (o2,o2) is set
the Arrows of C . [o2,o2] is set
[:<^o2,o2^>,<^(o1 . o2),(o1 . o2)^>:] is Relation-like non empty set
bool [:<^o2,o2^>,<^(o1 . o2),(o1 . o2)^>:] is non empty set
the MorphMap of o1 . (o2,o2) is set
the MorphMap of o1 . [o2,o2] is Relation-like Function-like set
proj1 (Morph-Map (o1,o2,o2)) is set
idm o2 is retraction coretraction mono epi M2(<^o2,o2^>)
(Morph-Map (o1,o2,o2)) . (idm o2) is M2(<^(o1 . o2),(o1 . o2)^>)
o1 . (idm o2) is M2(<^(o1 . o2),(o1 . o2)^>)
o1 . n is M2(<^(o1 . o1),(o1 . o2)^>)
(o1 . n) * (o1 . o2) is M2(<^(o1 . o2),(o1 . o2)^>)
n * o2 is M2(<^o2,o2^>)
o1 . (n * o2) is M2(<^(o1 . o2),(o1 . o2)^>)
(Morph-Map (o1,o2,o2)) . (n * o2) is M2(<^(o1 . o2),(o1 . o2)^>)
C is non empty transitive V129() with_units reflexive AltCatStr
i is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o2 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o1 . o1 is M2( the carrier of i)
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o2 is M2(<^o2,o1^>)
o1 . o2 is M2(<^(o1 . o2),(o1 . o1)^>)
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
C is non empty transitive V129() with_units reflexive AltCatStr
i is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o2 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o1 . o1 is M2( the carrier of i)
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
o2 is M2(<^(o1 . o2),(o1 . o1)^>)
p1 is M2(<^o2,o1^>)
o1 . p1 is M2(<^(o1 . o2),(o1 . o1)^>)
C is non empty transitive with_units reflexive AltCatStr
i is non empty transitive with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o1 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o1 . o2 is M2( the carrier of i)
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o2 is M2(<^o2,o1^>)
o1 . o2 is M2(<^(o1 . o1),(o1 . o2)^>)
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
p1 is M2(<^(o1 . o2),(o1 . o1)^>)
Morph-Map (o1,o1,o2) is Relation-like <^o1,o2^> -defined <^(o1 . o2),(o1 . o1)^> -valued Function-like quasi_total M2( bool [:<^o1,o2^>,<^(o1 . o2),(o1 . o1)^>:])
[:<^o1,o2^>,<^(o1 . o2),(o1 . o1)^>:] is Relation-like set
bool [:<^o1,o2^>,<^(o1 . o2),(o1 . o1)^>:] is non empty set
the MorphMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) V36() V37() MSUnTrans of the ObjectMap of o1, the Arrows of C, the Arrows of i
the MorphMap of o1 . (o1,o2) is set
the MorphMap of o1 . [o1,o2] is Relation-like Function-like set
proj2 (Morph-Map (o1,o1,o2)) is set
proj1 (Morph-Map (o1,o1,o2)) is set
p2 is set
(Morph-Map (o1,o1,o2)) . p2 is set
n is M2(<^o1,o2^>)
(o1 . o2) * p1 is M2(<^(o1 . o2),(o1 . o2)^>)
<^(o1 . o2),(o1 . o2)^> is non empty set
the Arrows of i . ((o1 . o2),(o1 . o2)) is set
[(o1 . o2),(o1 . o2)] is V15() set
{(o1 . o2),(o1 . o2)} is set
{{(o1 . o2),(o1 . o2)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o2)] is set
idm (o1 . o2) is retraction coretraction mono epi M2(<^(o1 . o2),(o1 . o2)^>)
Morph-Map (o1,o2,o2) is Relation-like <^o2,o2^> -defined <^(o1 . o2),(o1 . o2)^> -valued Function-like quasi_total M2( bool [:<^o2,o2^>,<^(o1 . o2),(o1 . o2)^>:])
<^o2,o2^> is non empty set
the Arrows of C . (o2,o2) is set
the Arrows of C . [o2,o2] is set
[:<^o2,o2^>,<^(o1 . o2),(o1 . o2)^>:] is Relation-like non empty set
bool [:<^o2,o2^>,<^(o1 . o2),(o1 . o2)^>:] is non empty set
the MorphMap of o1 . (o2,o2) is set
the MorphMap of o1 . [o2,o2] is Relation-like Function-like set
proj1 (Morph-Map (o1,o2,o2)) is set
idm o2 is retraction coretraction mono epi M2(<^o2,o2^>)
(Morph-Map (o1,o2,o2)) . (idm o2) is M2(<^(o1 . o2),(o1 . o2)^>)
o1 . (idm o2) is M2(<^(o1 . o2),(o1 . o2)^>)
o1 . n is M2(<^(o1 . o2),(o1 . o1)^>)
(o1 . o2) * (o1 . n) is M2(<^(o1 . o2),(o1 . o2)^>)
n * o2 is M2(<^o2,o2^>)
o1 . (n * o2) is M2(<^(o1 . o2),(o1 . o2)^>)
(Morph-Map (o1,o2,o2)) . (n * o2) is M2(<^(o1 . o2),(o1 . o2)^>)
C is non empty transitive with_units reflexive AltCatStr
i is non empty transitive with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o1 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o1 . o2 is M2( the carrier of i)
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o2 is M2(<^o2,o1^>)
o1 . o2 is M2(<^(o1 . o1),(o1 . o2)^>)
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
p1 is M2(<^(o1 . o2),(o1 . o1)^>)
Morph-Map (o1,o1,o2) is Relation-like <^o1,o2^> -defined <^(o1 . o2),(o1 . o1)^> -valued Function-like quasi_total M2( bool [:<^o1,o2^>,<^(o1 . o2),(o1 . o1)^>:])
[:<^o1,o2^>,<^(o1 . o2),(o1 . o1)^>:] is Relation-like set
bool [:<^o1,o2^>,<^(o1 . o2),(o1 . o1)^>:] is non empty set
the MorphMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) V36() V37() MSUnTrans of the ObjectMap of o1, the Arrows of C, the Arrows of i
the MorphMap of o1 . (o1,o2) is set
the MorphMap of o1 . [o1,o2] is Relation-like Function-like set
proj2 (Morph-Map (o1,o1,o2)) is set
proj1 (Morph-Map (o1,o1,o2)) is set
p2 is set
(Morph-Map (o1,o1,o2)) . p2 is set
n is M2(<^o1,o2^>)
p1 * (o1 . o2) is M2(<^(o1 . o1),(o1 . o1)^>)
<^(o1 . o1),(o1 . o1)^> is non empty set
the Arrows of i . ((o1 . o1),(o1 . o1)) is set
[(o1 . o1),(o1 . o1)] is V15() set
{(o1 . o1),(o1 . o1)} is set
{{(o1 . o1),(o1 . o1)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o1)] is set
idm (o1 . o1) is retraction coretraction mono epi M2(<^(o1 . o1),(o1 . o1)^>)
Morph-Map (o1,o1,o1) is Relation-like <^o1,o1^> -defined <^(o1 . o1),(o1 . o1)^> -valued Function-like quasi_total M2( bool [:<^o1,o1^>,<^(o1 . o1),(o1 . o1)^>:])
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
the Arrows of C . [o1,o1] is set
[:<^o1,o1^>,<^(o1 . o1),(o1 . o1)^>:] is Relation-like non empty set
bool [:<^o1,o1^>,<^(o1 . o1),(o1 . o1)^>:] is non empty set
the MorphMap of o1 . (o1,o1) is set
the MorphMap of o1 . [o1,o1] is Relation-like Function-like set
proj1 (Morph-Map (o1,o1,o1)) is set
idm o1 is retraction coretraction mono epi M2(<^o1,o1^>)
(Morph-Map (o1,o1,o1)) . (idm o1) is M2(<^(o1 . o1),(o1 . o1)^>)
o1 . (idm o1) is M2(<^(o1 . o1),(o1 . o1)^>)
o1 . n is M2(<^(o1 . o2),(o1 . o1)^>)
(o1 . n) * (o1 . o2) is M2(<^(o1 . o1),(o1 . o1)^>)
o2 * n is M2(<^o1,o1^>)
o1 . (o2 * n) is M2(<^(o1 . o1),(o1 . o1)^>)
(Morph-Map (o1,o1,o1)) . (o2 * n) is M2(<^(o1 . o1),(o1 . o1)^>)
C is non empty transitive V129() with_units reflexive AltCatStr
i is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o1 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o1 . o2 is M2( the carrier of i)
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
o2 is M2(<^o2,o1^>)
o1 . o2 is M2(<^(o1 . o1),(o1 . o2)^>)
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
<^(o1 . o2),(o1 . o1)^> is set
the Arrows of i . ((o1 . o2),(o1 . o1)) is set
[(o1 . o2),(o1 . o1)] is V15() set
{(o1 . o2),(o1 . o1)} is set
{(o1 . o2)} is set
{{(o1 . o2),(o1 . o1)},{(o1 . o2)}} is set
the Arrows of i . [(o1 . o2),(o1 . o1)] is set
C is non empty transitive V129() with_units reflexive AltCatStr
i is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
o1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of C,i
o2 is M2( the carrier of C)
o1 is M2( the carrier of C)
<^o2,o1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 . o1 is M2( the carrier of i)
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the ObjectMap of o1 is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of i, the carrier of i:] -valued Function-like quasi_total M2( bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:])
[:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of i, the carrier of i:]:] is non empty set
the ObjectMap of o1 . (o1,o1) is M2([: the carrier of i, the carrier of i:])
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the ObjectMap of o1 . [o1,o1] is set
K40(( the ObjectMap of o1 . (o1,o1))) is set
o1 . o2 is M2( the carrier of i)
the ObjectMap of o1 . (o2,o2) is M2([: the carrier of i, the carrier of i:])
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the ObjectMap of o1 . [o2,o2] is set
K40(( the ObjectMap of o1 . (o2,o2))) is set
<^(o1 . o1),(o1 . o2)^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
the Arrows of i . ((o1 . o1),(o1 . o2)) is set
[(o1 . o1),(o1 . o2)] is V15() set
{(o1 . o1),(o1 . o2)} is set
{(o1 . o1)} is set
{{(o1 . o1),(o1 . o2)},{(o1 . o1)}} is set
the Arrows of i . [(o1 . o1),(o1 . o2)] is set
o2 is M2(<^(o1 . o1),(o1 . o2)^>)
p1 is M2(<^o2,o1^>)
o1 . p1 is M2(<^(o1 . o1),(o1 . o2)^>)
C is non empty transitive AltCatStr
the carrier of C is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
i is M2( the carrier of C)
o2 is M2( the carrier of C)
the Arrows of C . (i,o2) is set
[i,o2] is V15() set
{i,o2} is set
{i} is set
{{i,o2},{i}} is set
the Arrows of C . [i,o2] is set
o1 is M2( the carrier of C)
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
the Arrows of C . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{{i,o1},{i}} is set
the Arrows of C . [i,o1] is set
[:( the Arrows of C . (o1,o2)),( the Arrows of C . (i,o1)):] is Relation-like set
o1 is set
o2 is set
p1 is set
[o2,p1] is V15() set
{o2,p1} is set
{o2} is set
{{o2,p1},{o2}} is set
<^o1,o2^> is set
<^i,o1^> is set
<^i,o2^> is set
C is AltCatStr
the carrier of C is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like set
i is SubCatStr of C
the carrier of i is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like V14([: the carrier of i, the carrier of i:]) set
[: the carrier of i, the carrier of i:] is Relation-like set
proj1 the Arrows of C is set
the Arrows of C || the carrier of i is set
the Arrows of C | [: the carrier of i, the carrier of i:] is Relation-like [: the carrier of i, the carrier of i:] -defined [: the carrier of C, the carrier of C:] -defined Function-like set
C is non empty with_units reflexive AltCatStr
the carrier of C is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
i is SubCatStr of C
the carrier of i is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like V14([: the carrier of i, the carrier of i:]) set
[: the carrier of i, the carrier of i:] is Relation-like set
o1 is non empty full SubCatStr of C
the carrier of o1 is non empty set
o2 is M2( the carrier of o1)
o1 is M2( the carrier of C)
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
<^o2,o2^> is set
the Arrows of o1 is Relation-like [: the carrier of o1, the carrier of o1:] -defined Function-like non empty V14([: the carrier of o1, the carrier of o1:]) set
[: the carrier of o1, the carrier of o1:] is Relation-like non empty set
the Arrows of o1 . (o2,o2) is set
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the Arrows of o1 . [o2,o2] is set
idm o1 is retraction coretraction mono epi M2(<^o1,o1^>)
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Comp of C is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {| the Arrows of C, the Arrows of C|},{| the Arrows of C|}
[: the carrier of C, the carrier of C, the carrier of C:] is non empty set
{| the Arrows of C, the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{| the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
AltCatStr(# the carrier of C, the Arrows of C, the Comp of C #) is non empty strict AltCatStr
i is SubCatStr of C
o1 is non empty transitive V129() with_units reflexive full id-inheriting SubCatStr of C
C is non empty transitive V129() with_units reflexive AltCatStr
i is non empty transitive V129() with_units reflexive id-inheriting SubCatStr of C
o1 is non empty transitive V129() with_units reflexive id-inheriting SubCatStr of i
o2 is non empty with_units reflexive SubCatStr of C
the carrier of o2 is non empty set
the carrier of C is non empty set
o1 is M2( the carrier of o2)
o2 is M2( the carrier of C)
the carrier of i is non empty set
idm o1 is retraction coretraction mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of o2 is Relation-like [: the carrier of o2, the carrier of o2:] -defined Function-like non empty V14([: the carrier of o2, the carrier of o2:]) set
[: the carrier of o2, the carrier of o2:] is Relation-like non empty set
the Arrows of o2 . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of o2 . [o1,o1] is set
p1 is M2( the carrier of i)
idm p1 is retraction coretraction iso mono epi M2(<^p1,p1^>)
<^p1,p1^> is non empty set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i . (p1,p1) is set
[p1,p1] is V15() set
{p1,p1} is set
{p1} is set
{{p1,p1},{p1}} is set
the Arrows of i . [p1,p1] is set
idm o2 is retraction coretraction iso mono epi M2(<^o2,o2^>)
<^o2,o2^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o2,o2) is set
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the Arrows of C . [o2,o2] is set
C is non empty transitive AltCatStr
the carrier of C is non empty set
i is non empty transitive SubCatStr of C
the carrier of i is non empty set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
<^o1,o2^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 is M2( the carrier of i)
o2 is M2( the carrier of i)
<^o1,o2^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of i . [o1,o2] is set
p1 is M2(<^o1,o2^>)
p2 is M2(<^o1,o2^>)
n is M2( the carrier of i)
<^n,o1^> is set
the Arrows of i . (n,o1) is set
[n,o1] is V15() set
{n,o1} is set
{n} is set
{{n,o1},{n}} is set
the Arrows of i . [n,o1] is set
n2 is M2( the carrier of C)
<^n2,o1^> is set
the Arrows of C . (n2,o1) is set
[n2,o1] is V15() set
{n2,o1} is set
{n2} is set
{{n2,o1},{n2}} is set
the Arrows of C . [n2,o1] is set
n1 is M2(<^n,o1^>)
p2 * n1 is M2(<^n,o2^>)
<^n,o2^> is set
the Arrows of i . (n,o2) is set
[n,o2] is V15() set
{n,o2} is set
{{n,o2},{n}} is set
the Arrows of i . [n,o2] is set
n2 is M2(<^n,o1^>)
p2 * n2 is M2(<^n,o2^>)
n1 is M2(<^n2,o1^>)
p1 * n1 is M2(<^n2,o2^>)
<^n2,o2^> is set
the Arrows of C . (n2,o2) is set
[n2,o2] is V15() set
{n2,o2} is set
{{n2,o2},{n2}} is set
the Arrows of C . [n2,o2] is set
p2 is M2(<^n2,o1^>)
p1 * p2 is M2(<^n2,o2^>)
n is M2( the carrier of i)
<^o2,n^> is set
the Arrows of i . (o2,n) is set
[o2,n] is V15() set
{o2,n} is set
{o2} is set
{{o2,n},{o2}} is set
the Arrows of i . [o2,n] is set
n2 is M2( the carrier of C)
<^o2,n2^> is set
the Arrows of C . (o2,n2) is set
[o2,n2] is V15() set
{o2,n2} is set
{o2} is set
{{o2,n2},{o2}} is set
the Arrows of C . [o2,n2] is set
n1 is M2(<^o2,n^>)
n1 * p2 is M2(<^o1,n^>)
<^o1,n^> is set
the Arrows of i . (o1,n) is set
[o1,n] is V15() set
{o1,n} is set
{{o1,n},{o1}} is set
the Arrows of i . [o1,n] is set
n2 is M2(<^o2,n^>)
n2 * p2 is M2(<^o1,n^>)
n1 is M2(<^o2,n2^>)
n1 * p1 is M2(<^o1,n2^>)
<^o1,n2^> is set
the Arrows of C . (o1,n2) is set
[o1,n2] is V15() set
{o1,n2} is set
{{o1,n2},{o1}} is set
the Arrows of C . [o1,n2] is set
p2 is M2(<^o2,n2^>)
p2 * p1 is M2(<^o1,n2^>)
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
i is non empty transitive V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of i is non empty set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
<^o1,o2^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
o1 is M2( the carrier of i)
o2 is M2( the carrier of i)
<^o1,o2^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of i . [o1,o2] is set
<^o2,o1^> is set
the Arrows of i . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of i . [o2,o1] is set
p1 is M2(<^o1,o2^>)
p2 is M2(<^o2,o1^>)
n is M2(<^o1,o2^>)
n2 is M2(<^o2,o1^>)
n * n2 is M2(<^o2,o2^>)
<^o2,o2^> is non empty set
the Arrows of i . (o2,o2) is set
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the Arrows of i . [o2,o2] is set
p1 * p2 is M2(<^o2,o2^>)
<^o2,o2^> is non empty set
the Arrows of C . (o2,o2) is set
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the Arrows of C . [o2,o2] is set
idm o2 is retraction coretraction iso mono epi M2(<^o2,o2^>)
idm o2 is retraction coretraction iso mono epi M2(<^o2,o2^>)
p1 * p2 is M2(<^o2,o2^>)
<^o2,o2^> is non empty set
the Arrows of C . (o2,o2) is set
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the Arrows of C . [o2,o2] is set
n * n2 is M2(<^o2,o2^>)
<^o2,o2^> is non empty set
the Arrows of i . (o2,o2) is set
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the Arrows of i . [o2,o2] is set
idm o2 is retraction coretraction iso mono epi M2(<^o2,o2^>)
idm o2 is retraction coretraction iso mono epi M2(<^o2,o2^>)
n2 * n is M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of i . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of i . [o1,o1] is set
p2 * p1 is M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
p2 * p1 is M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
n2 * n is M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of i . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of i . [o1,o1] is set
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
i is non empty transitive V129() with_units reflexive full id-inheriting SubCatStr of C
the carrier of i is non empty set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
<^o1,o2^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 is M2( the carrier of i)
o2 is M2( the carrier of i)
<^o1,o2^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of i . [o1,o2] is set
<^o2,o1^> is set
the Arrows of i . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of i . [o2,o1] is set
p1 is M2(<^o1,o2^>)
p2 is M2(<^o1,o2^>)
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
n is M2(<^o2,o1^>)
n2 is M2(<^o2,o1^>)
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
n is M2(<^o2,o1^>)
n2 is M2(<^o2,o1^>)
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
i is non empty transitive V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of i is non empty set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
<^o1,o2^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
o1 is M2( the carrier of i)
o2 is M2( the carrier of i)
<^o1,o2^> is set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of i . [o1,o2] is set
<^o2,o1^> is set
the Arrows of i . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of i . [o2,o1] is set
p1 is M2(<^o1,o2^>)
p2 is M2(<^o1,o2^>)
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
n is M2(<^o2,o1^>)
n2 is M2(<^o2,o1^>)
n is M2(<^o2,o1^>)
n2 is M2(<^o2,o1^>)
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
o1 is set
o2 is set
o1 is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
o2 is M2( the carrier of C)
p1 is M2( the carrier of C)
<^o2,p1^> is set
the Arrows of C . (o2,p1) is set
[o2,p1] is V15() set
{o2,p1} is set
{o2} is set
{{o2,p1},{o2}} is set
the Arrows of C . [o2,p1] is set
p2 is set
n is set
n2 is M2(<^o2,p1^>)
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
<^n2,n1^> is set
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
n2 is M2(<^n2,n1^>)
o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Comp of C is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {| the Arrows of C, the Arrows of C|},{| the Arrows of C|}
[: the carrier of C, the carrier of C, the carrier of C:] is non empty set
{| the Arrows of C, the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{| the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o2 is set
o1 is set
o2 is set
p1 is set
[o1,o2,p1] is V15() V16() set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
[[o1,o2],p1] is V15() set
{[o1,o2],p1} is set
{[o1,o2]} is Relation-like Function-like set
{{[o1,o2],p1},{[o1,o2]}} is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
n2 is M2( the carrier of C)
the Comp of C . (p2,n,n2) is Relation-like [:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] -defined the Arrows of C . (p2,n2) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):])
the Arrows of C . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of C . [n,n2] is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] is Relation-like set
the Arrows of C . (p2,n2) is set
[p2,n2] is V15() set
{p2,n2} is set
{{p2,n2},{p2}} is set
the Arrows of C . [p2,n2] is set
[:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):] is Relation-like set
bool [:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):] is non empty set
o1 . (n,n2) is set
o1 . [n,n2] is set
o1 . (p2,n) is set
o1 . [p2,n] is set
[:(o1 . (n,n2)),(o1 . (p2,n)):] is Relation-like set
( the Comp of C . (p2,n,n2)) | [:(o1 . (n,n2)),(o1 . (p2,n)):] is Relation-like [:(o1 . (n,n2)),(o1 . (p2,n)):] -defined [:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] -defined the Arrows of C . (p2,n2) -valued Function-like set
[p2,n,n2] is V15() V16() set
[[p2,n],n2] is V15() set
{[p2,n],n2} is set
{[p2,n]} is Relation-like Function-like set
{{[p2,n],n2},{[p2,n]}} is set
o2 is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o1 is set
o1 . o1 is set
the Arrows of C . o1 is set
o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n is M2(<^p1,p2^>)
{|o1,o1|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{|o1|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o1 is set
o2 . o1 is set
{|o1,o1|} . o1 is set
{|o1|} . o1 is set
[:({|o1,o1|} . o1),({|o1|} . o1):] is Relation-like set
bool [:({|o1,o1|} . o1),({|o1|} . o1):] is non empty set
o2 is M2( the carrier of C)
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
[o2,p1,p2] is V15() V16() set
[o2,p1] is V15() set
{o2,p1} is set
{o2} is set
{{o2,p1},{o2}} is set
[[o2,p1],p2] is V15() set
{[o2,p1],p2} is set
{[o2,p1]} is Relation-like Function-like set
{{[o2,p1],p2},{[o2,p1]}} is set
the Comp of C . (o2,p1,p2) is Relation-like [:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):])
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
the Arrows of C . (o2,p1) is set
the Arrows of C . [o2,p1] is set
[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] is Relation-like set
the Arrows of C . (o2,p2) is set
[o2,p2] is V15() set
{o2,p2} is set
{{o2,p2},{o2}} is set
the Arrows of C . [o2,p2] is set
[:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):] is Relation-like set
bool [:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):] is non empty set
o1 . (p1,p2) is set
o1 . [p1,p2] is set
o1 . (o2,p1) is set
o1 . [o2,p1] is set
[:(o1 . (p1,p2)),(o1 . (o2,p1)):] is Relation-like set
( the Comp of C . (o2,p1,p2)) | [:(o1 . (p1,p2)),(o1 . (o2,p1)):] is Relation-like [:(o1 . (p1,p2)),(o1 . (o2,p1)):] -defined [:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like set
[:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):] is Relation-like set
bool [:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):] is non empty set
n2 is set
n1 is set
n2 is set
[n1,n2] is V15() set
{n1,n2} is set
{n1} is set
{{n1,n2},{n1}} is set
<^p1,p2^> is set
<^o2,p1^> is set
<^o2,p2^> is set
{|o1|} . (o2,p1,p2) is set
o1 . (o2,p2) is set
o1 . [o2,p2] is set
n is Relation-like [:(o1 . (p1,p2)),(o1 . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like quasi_total M2( bool [:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):])
proj2 n is set
n2 is set
proj1 n is Relation-like set
n1 is set
n . n1 is set
n2 is set
n1 is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
<^p2,n^> is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
qq is M2(<^p2,n^>)
r1 is M2( the carrier of C)
r2 is M2( the carrier of C)
<^r1,r2^> is set
the Arrows of C . (r1,r2) is set
[r1,r2] is V15() set
{r1,r2} is set
{r1} is set
{{r1,r2},{r1}} is set
the Arrows of C . [r1,r2] is set
rr is M2(<^r1,r2^>)
<^r2,n^> is set
the Arrows of C . (r2,n) is set
[r2,n] is V15() set
{r2,n} is set
{r2} is set
{{r2,n},{r2}} is set
the Arrows of C . [r2,n] is set
<^r1,n^> is set
the Arrows of C . (r1,n) is set
[r1,n] is V15() set
{r1,n} is set
{{r1,n},{r1}} is set
the Arrows of C . [r1,n] is set
mm is M2(<^r2,n^>)
mm * rr is M2(<^r1,n^>)
( the Comp of C . (o2,p1,p2)) . (mm,rr) is set
[mm,rr] is V15() set
{mm,rr} is set
{mm} is set
{{mm,rr},{mm}} is set
( the Comp of C . (o2,p1,p2)) . [mm,rr] is set
mm is M2( the carrier of C)
c₂₁ is M2( the carrier of C)
<^mm,c₂₁^> is set
the Arrows of C . (mm,c₂₁) is set
[mm,c₂₁] is V15() set
{mm,c₂₁} is set
{mm} is set
{{mm,c₂₁},{mm}} is set
the Arrows of C . [mm,c₂₁] is set
c₂₂ is M2(<^mm,c₂₁^>)
{|o1,o1|} . (o2,p1,p2) is set
o1 is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {|o1,o1|},{|o1|}
AltCatStr(# the carrier of C,o1,o1 #) is non empty strict AltCatStr
the carrier of AltCatStr(# the carrier of C,o1,o1 #) is non empty set
[: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] is Relation-like non empty set
the Arrows of AltCatStr(# the carrier of C,o1,o1 #) is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
[: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] is non empty set
the Comp of AltCatStr(# the carrier of C,o1,o1 #) is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) V36() V37() ManySortedFunction of {| the Arrows of AltCatStr(# the carrier of C,o1,o1 #), the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|},{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|}
{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #), the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|} is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|} is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
p2 is set
the Comp of AltCatStr(# the carrier of C,o1,o1 #) . p2 is Relation-like Function-like set
the Comp of C . p2 is Relation-like Function-like set
o1 . p2 is Relation-like Function-like set
n is M2( the carrier of C)
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
[n,n2,n1] is V15() V16() set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
[[n,n2],n1] is V15() set
{[n,n2],n1} is set
{[n,n2]} is Relation-like Function-like set
{{[n,n2],n1},{[n,n2]}} is set
the Comp of C . (n,n2,n1) is Relation-like [:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] -defined the Arrows of C . (n,n1) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):])
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
the Arrows of C . (n,n2) is set
the Arrows of C . [n,n2] is set
[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] is Relation-like set
the Arrows of C . (n,n1) is set
[n,n1] is V15() set
{n,n1} is set
{{n,n1},{n}} is set
the Arrows of C . [n,n1] is set
[:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):] is Relation-like set
bool [:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):] is non empty set
o1 . (n2,n1) is set
o1 . [n2,n1] is set
o1 . (n,n2) is set
o1 . [n,n2] is set
[:(o1 . (n2,n1)),(o1 . (n,n2)):] is Relation-like set
( the Comp of C . (n,n2,n1)) | [:(o1 . (n2,n1)),(o1 . (n,n2)):] is Relation-like [:(o1 . (n2,n1)),(o1 . (n,n2)):] -defined [:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] -defined the Arrows of C . (n,n1) -valued Function-like set
n2 is set
p2 is non empty strict SubCatStr of C
the carrier of p2 is non empty set
n is M2( the carrier of p2)
n2 is M2( the carrier of p2)
<^n,n2^> is set
the Arrows of p2 is Relation-like [: the carrier of p2, the carrier of p2:] -defined Function-like non empty V14([: the carrier of p2, the carrier of p2:]) set
[: the carrier of p2, the carrier of p2:] is Relation-like non empty set
the Arrows of p2 . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of p2 . [n,n2] is set
n1 is M2( the carrier of p2)
<^n2,n1^> is set
the Arrows of p2 . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of p2 . [n2,n1] is set
<^n,n1^> is set
the Arrows of p2 . (n,n1) is set
[n,n1] is V15() set
{n,n1} is set
{{n,n1},{n}} is set
the Arrows of p2 . [n,n1] is set
n2 is set
n1 is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
<^p2,n^> is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
qq is M2(<^p2,n^>)
r1 is M2( the carrier of C)
r2 is M2( the carrier of C)
<^r1,r2^> is set
the Arrows of C . (r1,r2) is set
[r1,r2] is V15() set
{r1,r2} is set
{r1} is set
{{r1,r2},{r1}} is set
the Arrows of C . [r1,r2] is set
rr is M2(<^r1,r2^>)
<^r2,n^> is set
the Arrows of C . (r2,n) is set
[r2,n] is V15() set
{r2,n} is set
{r2} is set
{{r2,n},{r2}} is set
the Arrows of C . [r2,n] is set
mm is M2(<^r2,n^>)
mm * rr is M2(<^r1,n^>)
<^r1,n^> is set
the Arrows of C . (r1,n) is set
[r1,n] is V15() set
{r1,n} is set
{{r1,n},{r1}} is set
the Arrows of C . [r1,n] is set
c₂₁ is M2( the carrier of C)
c₂₂ is M2( the carrier of C)
<^c₂₁,c₂₂^> is set
the Arrows of C . (c₂₁,c₂₂) is set
[c₂₁,c₂₂] is V15() set
{c₂₁,c₂₂} is set
{c₂₁} is set
{{c₂₁,c₂₂},{c₂₁}} is set
the Arrows of C . [c₂₁,c₂₂] is set
c₂₃ is M2(<^c₂₁,c₂₂^>)
n is non empty transitive strict V129() SubCatStr of C
the carrier of n is non empty set
[: the carrier of n, the carrier of n:] is Relation-like non empty set
the Arrows of n is Relation-like [: the carrier of n, the carrier of n:] -defined Function-like non empty V14([: the carrier of n, the carrier of n:]) set
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
<^n2,n1^> is set
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
the Arrows of n . (n2,n1) is set
the Arrows of n . [n2,n1] is set
n2 is M2(<^n2,n1^>)
n1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^n1,p2^> is set
the Arrows of C . (n1,p2) is set
[n1,p2] is V15() set
{n1,p2} is set
{n1} is set
{{n1,p2},{n1}} is set
the Arrows of C . [n1,p2] is set
n is M2(<^n1,p2^>)
i is non empty transitive strict V129() SubCatStr of C
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
o1 is non empty transitive strict V129() SubCatStr of C
the carrier of o1 is non empty set
[: the carrier of o1, the carrier of o1:] is Relation-like non empty set
the Arrows of o1 is Relation-like [: the carrier of o1, the carrier of o1:] -defined Function-like non empty V14([: the carrier of o1, the carrier of o1:]) set
o2 is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of i . o2 is set
the Arrows of o1 . o2 is set
n is set
the Arrows of C . o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^p1,p2^>)
the Arrows of i . (p1,p2) is set
the Arrows of i . [p1,p2] is set
the Arrows of o1 . (p1,p2) is set
the Arrows of o1 . [p1,p2] is set
n is set
the Arrows of C . o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^p1,p2^>)
the Arrows of o1 . (p1,p2) is set
the Arrows of o1 . [p1,p2] is set
the Arrows of i . (p1,p2) is set
the Arrows of i . [p1,p2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() SubCatStr of C
the carrier of (C) is non empty set
the carrier of C is non empty set
i is M2( the carrier of (C))
o1 is M2( the carrier of C)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
<^i,i^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (i,i) is set
[i,i] is V15() set
{i,i} is set
{i} is set
{{i,i},{i}} is set
the Arrows of (C) . [i,i] is set
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
o1 is set
o2 is set
o1 is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
o2 is M2( the carrier of C)
p1 is M2( the carrier of C)
<^o2,p1^> is set
the Arrows of C . (o2,p1) is set
[o2,p1] is V15() set
{o2,p1} is set
{o2} is set
{{o2,p1},{o2}} is set
the Arrows of C . [o2,p1] is set
p2 is set
n is set
n2 is M2(<^o2,p1^>)
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
<^n2,n1^> is set
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
n2 is M2(<^n2,n1^>)
o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Comp of C is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {| the Arrows of C, the Arrows of C|},{| the Arrows of C|}
[: the carrier of C, the carrier of C, the carrier of C:] is non empty set
{| the Arrows of C, the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{| the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o2 is set
o1 is set
o2 is set
p1 is set
[o1,o2,p1] is V15() V16() set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
[[o1,o2],p1] is V15() set
{[o1,o2],p1} is set
{[o1,o2]} is Relation-like Function-like set
{{[o1,o2],p1},{[o1,o2]}} is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
n2 is M2( the carrier of C)
the Comp of C . (p2,n,n2) is Relation-like [:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] -defined the Arrows of C . (p2,n2) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):])
the Arrows of C . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of C . [n,n2] is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] is Relation-like set
the Arrows of C . (p2,n2) is set
[p2,n2] is V15() set
{p2,n2} is set
{{p2,n2},{p2}} is set
the Arrows of C . [p2,n2] is set
[:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):] is Relation-like set
bool [:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):] is non empty set
o1 . (n,n2) is set
o1 . [n,n2] is set
o1 . (p2,n) is set
o1 . [p2,n] is set
[:(o1 . (n,n2)),(o1 . (p2,n)):] is Relation-like set
( the Comp of C . (p2,n,n2)) | [:(o1 . (n,n2)),(o1 . (p2,n)):] is Relation-like [:(o1 . (n,n2)),(o1 . (p2,n)):] -defined [:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] -defined the Arrows of C . (p2,n2) -valued Function-like set
[p2,n,n2] is V15() V16() set
[[p2,n],n2] is V15() set
{[p2,n],n2} is set
{[p2,n]} is Relation-like Function-like set
{{[p2,n],n2},{[p2,n]}} is set
o2 is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o1 is set
o1 . o1 is set
the Arrows of C . o1 is set
o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n is M2(<^p1,p2^>)
{|o1,o1|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{|o1|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o1 is set
o2 . o1 is set
{|o1,o1|} . o1 is set
{|o1|} . o1 is set
[:({|o1,o1|} . o1),({|o1|} . o1):] is Relation-like set
bool [:({|o1,o1|} . o1),({|o1|} . o1):] is non empty set
o2 is M2( the carrier of C)
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
[o2,p1,p2] is V15() V16() set
[o2,p1] is V15() set
{o2,p1} is set
{o2} is set
{{o2,p1},{o2}} is set
[[o2,p1],p2] is V15() set
{[o2,p1],p2} is set
{[o2,p1]} is Relation-like Function-like set
{{[o2,p1],p2},{[o2,p1]}} is set
the Comp of C . (o2,p1,p2) is Relation-like [:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):])
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
the Arrows of C . (o2,p1) is set
the Arrows of C . [o2,p1] is set
[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] is Relation-like set
the Arrows of C . (o2,p2) is set
[o2,p2] is V15() set
{o2,p2} is set
{{o2,p2},{o2}} is set
the Arrows of C . [o2,p2] is set
[:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):] is Relation-like set
bool [:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):] is non empty set
o1 . (p1,p2) is set
o1 . [p1,p2] is set
o1 . (o2,p1) is set
o1 . [o2,p1] is set
[:(o1 . (p1,p2)),(o1 . (o2,p1)):] is Relation-like set
( the Comp of C . (o2,p1,p2)) | [:(o1 . (p1,p2)),(o1 . (o2,p1)):] is Relation-like [:(o1 . (p1,p2)),(o1 . (o2,p1)):] -defined [:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like set
[:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):] is Relation-like set
bool [:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):] is non empty set
n2 is set
n1 is set
n2 is set
[n1,n2] is V15() set
{n1,n2} is set
{n1} is set
{{n1,n2},{n1}} is set
<^p1,p2^> is set
<^o2,p1^> is set
<^o2,p2^> is set
{|o1|} . (o2,p1,p2) is set
o1 . (o2,p2) is set
o1 . [o2,p2] is set
n is Relation-like [:(o1 . (p1,p2)),(o1 . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like quasi_total M2( bool [:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):])
proj2 n is set
n2 is set
proj1 n is Relation-like set
n1 is set
n . n1 is set
n2 is set
n1 is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
<^p2,n^> is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
qq is M2(<^p2,n^>)
r1 is M2( the carrier of C)
r2 is M2( the carrier of C)
<^r1,r2^> is set
the Arrows of C . (r1,r2) is set
[r1,r2] is V15() set
{r1,r2} is set
{r1} is set
{{r1,r2},{r1}} is set
the Arrows of C . [r1,r2] is set
rr is M2(<^r1,r2^>)
<^r2,n^> is set
the Arrows of C . (r2,n) is set
[r2,n] is V15() set
{r2,n} is set
{r2} is set
{{r2,n},{r2}} is set
the Arrows of C . [r2,n] is set
<^r1,n^> is set
the Arrows of C . (r1,n) is set
[r1,n] is V15() set
{r1,n} is set
{{r1,n},{r1}} is set
the Arrows of C . [r1,n] is set
mm is M2(<^r2,n^>)
mm * rr is M2(<^r1,n^>)
( the Comp of C . (o2,p1,p2)) . (mm,rr) is set
[mm,rr] is V15() set
{mm,rr} is set
{mm} is set
{{mm,rr},{mm}} is set
( the Comp of C . (o2,p1,p2)) . [mm,rr] is set
mm is M2( the carrier of C)
c₂₁ is M2( the carrier of C)
<^mm,c₂₁^> is set
the Arrows of C . (mm,c₂₁) is set
[mm,c₂₁] is V15() set
{mm,c₂₁} is set
{mm} is set
{{mm,c₂₁},{mm}} is set
the Arrows of C . [mm,c₂₁] is set
c₂₂ is M2(<^mm,c₂₁^>)
{|o1,o1|} . (o2,p1,p2) is set
o1 is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {|o1,o1|},{|o1|}
AltCatStr(# the carrier of C,o1,o1 #) is non empty strict AltCatStr
the carrier of AltCatStr(# the carrier of C,o1,o1 #) is non empty set
[: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] is Relation-like non empty set
the Arrows of AltCatStr(# the carrier of C,o1,o1 #) is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
[: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] is non empty set
the Comp of AltCatStr(# the carrier of C,o1,o1 #) is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) V36() V37() ManySortedFunction of {| the Arrows of AltCatStr(# the carrier of C,o1,o1 #), the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|},{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|}
{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #), the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|} is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|} is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
p2 is set
the Comp of AltCatStr(# the carrier of C,o1,o1 #) . p2 is Relation-like Function-like set
the Comp of C . p2 is Relation-like Function-like set
o1 . p2 is Relation-like Function-like set
n is M2( the carrier of C)
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
[n,n2,n1] is V15() V16() set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
[[n,n2],n1] is V15() set
{[n,n2],n1} is set
{[n,n2]} is Relation-like Function-like set
{{[n,n2],n1},{[n,n2]}} is set
the Comp of C . (n,n2,n1) is Relation-like [:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] -defined the Arrows of C . (n,n1) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):])
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
the Arrows of C . (n,n2) is set
the Arrows of C . [n,n2] is set
[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] is Relation-like set
the Arrows of C . (n,n1) is set
[n,n1] is V15() set
{n,n1} is set
{{n,n1},{n}} is set
the Arrows of C . [n,n1] is set
[:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):] is Relation-like set
bool [:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):] is non empty set
o1 . (n2,n1) is set
o1 . [n2,n1] is set
o1 . (n,n2) is set
o1 . [n,n2] is set
[:(o1 . (n2,n1)),(o1 . (n,n2)):] is Relation-like set
( the Comp of C . (n,n2,n1)) | [:(o1 . (n2,n1)),(o1 . (n,n2)):] is Relation-like [:(o1 . (n2,n1)),(o1 . (n,n2)):] -defined [:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] -defined the Arrows of C . (n,n1) -valued Function-like set
n2 is set
p2 is non empty strict SubCatStr of C
the carrier of p2 is non empty set
n is M2( the carrier of p2)
n2 is M2( the carrier of p2)
<^n,n2^> is set
the Arrows of p2 is Relation-like [: the carrier of p2, the carrier of p2:] -defined Function-like non empty V14([: the carrier of p2, the carrier of p2:]) set
[: the carrier of p2, the carrier of p2:] is Relation-like non empty set
the Arrows of p2 . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of p2 . [n,n2] is set
n1 is M2( the carrier of p2)
<^n2,n1^> is set
the Arrows of p2 . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of p2 . [n2,n1] is set
<^n,n1^> is set
the Arrows of p2 . (n,n1) is set
[n,n1] is V15() set
{n,n1} is set
{{n,n1},{n}} is set
the Arrows of p2 . [n,n1] is set
n2 is set
n1 is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
<^p2,n^> is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
qq is M2(<^p2,n^>)
r1 is M2( the carrier of C)
r2 is M2( the carrier of C)
<^r1,r2^> is set
the Arrows of C . (r1,r2) is set
[r1,r2] is V15() set
{r1,r2} is set
{r1} is set
{{r1,r2},{r1}} is set
the Arrows of C . [r1,r2] is set
rr is M2(<^r1,r2^>)
<^r2,n^> is set
the Arrows of C . (r2,n) is set
[r2,n] is V15() set
{r2,n} is set
{r2} is set
{{r2,n},{r2}} is set
the Arrows of C . [r2,n] is set
mm is M2(<^r2,n^>)
mm * rr is M2(<^r1,n^>)
<^r1,n^> is set
the Arrows of C . (r1,n) is set
[r1,n] is V15() set
{r1,n} is set
{{r1,n},{r1}} is set
the Arrows of C . [r1,n] is set
c₂₁ is M2( the carrier of C)
c₂₂ is M2( the carrier of C)
<^c₂₁,c₂₂^> is set
the Arrows of C . (c₂₁,c₂₂) is set
[c₂₁,c₂₂] is V15() set
{c₂₁,c₂₂} is set
{c₂₁} is set
{{c₂₁,c₂₂},{c₂₁}} is set
the Arrows of C . [c₂₁,c₂₂] is set
c₂₃ is M2(<^c₂₁,c₂₂^>)
n is non empty transitive strict V129() SubCatStr of C
the carrier of n is non empty set
[: the carrier of n, the carrier of n:] is Relation-like non empty set
the Arrows of n is Relation-like [: the carrier of n, the carrier of n:] -defined Function-like non empty V14([: the carrier of n, the carrier of n:]) set
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
<^n2,n1^> is set
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
the Arrows of n . (n2,n1) is set
the Arrows of n . [n2,n1] is set
n2 is M2(<^n2,n1^>)
n1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^n1,p2^> is set
the Arrows of C . (n1,p2) is set
[n1,p2] is V15() set
{n1,p2} is set
{n1} is set
{{n1,p2},{n1}} is set
the Arrows of C . [n1,p2] is set
n is M2(<^n1,p2^>)
i is non empty transitive strict V129() SubCatStr of C
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
o1 is non empty transitive strict V129() SubCatStr of C
the carrier of o1 is non empty set
[: the carrier of o1, the carrier of o1:] is Relation-like non empty set
the Arrows of o1 is Relation-like [: the carrier of o1, the carrier of o1:] -defined Function-like non empty V14([: the carrier of o1, the carrier of o1:]) set
o2 is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of i . o2 is set
the Arrows of o1 . o2 is set
n is set
the Arrows of C . o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^p1,p2^>)
the Arrows of i . (p1,p2) is set
the Arrows of i . [p1,p2] is set
the Arrows of o1 . (p1,p2) is set
the Arrows of o1 . [p1,p2] is set
n is set
the Arrows of C . o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^p1,p2^>)
the Arrows of o1 . (p1,p2) is set
the Arrows of o1 . [p1,p2] is set
the Arrows of i . (p1,p2) is set
the Arrows of i . [p1,p2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() SubCatStr of C
the carrier of (C) is non empty set
the carrier of C is non empty set
i is M2( the carrier of (C))
o1 is M2( the carrier of C)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
<^i,i^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (i,i) is set
[i,i] is V15() set
{i,i} is set
{i} is set
{{i,i},{i}} is set
the Arrows of (C) . [i,i] is set
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
o1 is set
o2 is set
o1 is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
o2 is M2( the carrier of C)
p1 is M2( the carrier of C)
<^o2,p1^> is set
the Arrows of C . (o2,p1) is set
[o2,p1] is V15() set
{o2,p1} is set
{o2} is set
{{o2,p1},{o2}} is set
the Arrows of C . [o2,p1] is set
<^p1,o2^> is set
the Arrows of C . (p1,o2) is set
[p1,o2] is V15() set
{p1,o2} is set
{p1} is set
{{p1,o2},{p1}} is set
the Arrows of C . [p1,o2] is set
p2 is set
n is set
n2 is M2(<^o2,p1^>)
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
<^n2,n1^> is set
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
<^n1,n2^> is set
the Arrows of C . (n1,n2) is set
[n1,n2] is V15() set
{n1,n2} is set
{n1} is set
{{n1,n2},{n1}} is set
the Arrows of C . [n1,n2] is set
n2 is M2(<^n2,n1^>)
o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Comp of C is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {| the Arrows of C, the Arrows of C|},{| the Arrows of C|}
[: the carrier of C, the carrier of C, the carrier of C:] is non empty set
{| the Arrows of C, the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{| the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o2 is set
o1 is set
o2 is set
p1 is set
[o1,o2,p1] is V15() V16() set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
[[o1,o2],p1] is V15() set
{[o1,o2],p1} is set
{[o1,o2]} is Relation-like Function-like set
{{[o1,o2],p1},{[o1,o2]}} is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
n2 is M2( the carrier of C)
the Comp of C . (p2,n,n2) is Relation-like [:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] -defined the Arrows of C . (p2,n2) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):])
the Arrows of C . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of C . [n,n2] is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] is Relation-like set
the Arrows of C . (p2,n2) is set
[p2,n2] is V15() set
{p2,n2} is set
{{p2,n2},{p2}} is set
the Arrows of C . [p2,n2] is set
[:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):] is Relation-like set
bool [:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):] is non empty set
o1 . (n,n2) is set
o1 . [n,n2] is set
o1 . (p2,n) is set
o1 . [p2,n] is set
[:(o1 . (n,n2)),(o1 . (p2,n)):] is Relation-like set
( the Comp of C . (p2,n,n2)) | [:(o1 . (n,n2)),(o1 . (p2,n)):] is Relation-like [:(o1 . (n,n2)),(o1 . (p2,n)):] -defined [:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] -defined the Arrows of C . (p2,n2) -valued Function-like set
[p2,n,n2] is V15() V16() set
[[p2,n],n2] is V15() set
{[p2,n],n2} is set
{[p2,n]} is Relation-like Function-like set
{{[p2,n],n2},{[p2,n]}} is set
o2 is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o1 is set
o1 . o1 is set
the Arrows of C . o1 is set
o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
<^p2,p1^> is set
the Arrows of C . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of C . [p2,p1] is set
n is M2(<^p1,p2^>)
{|o1,o1|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{|o1|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o1 is set
o2 . o1 is set
{|o1,o1|} . o1 is set
{|o1|} . o1 is set
[:({|o1,o1|} . o1),({|o1|} . o1):] is Relation-like set
bool [:({|o1,o1|} . o1),({|o1|} . o1):] is non empty set
o2 is M2( the carrier of C)
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
[o2,p1,p2] is V15() V16() set
[o2,p1] is V15() set
{o2,p1} is set
{o2} is set
{{o2,p1},{o2}} is set
[[o2,p1],p2] is V15() set
{[o2,p1],p2} is set
{[o2,p1]} is Relation-like Function-like set
{{[o2,p1],p2},{[o2,p1]}} is set
the Comp of C . (o2,p1,p2) is Relation-like [:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):])
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
the Arrows of C . (o2,p1) is set
the Arrows of C . [o2,p1] is set
[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] is Relation-like set
the Arrows of C . (o2,p2) is set
[o2,p2] is V15() set
{o2,p2} is set
{{o2,p2},{o2}} is set
the Arrows of C . [o2,p2] is set
[:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):] is Relation-like set
bool [:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):] is non empty set
o1 . (p1,p2) is set
o1 . [p1,p2] is set
o1 . (o2,p1) is set
o1 . [o2,p1] is set
[:(o1 . (p1,p2)),(o1 . (o2,p1)):] is Relation-like set
( the Comp of C . (o2,p1,p2)) | [:(o1 . (p1,p2)),(o1 . (o2,p1)):] is Relation-like [:(o1 . (p1,p2)),(o1 . (o2,p1)):] -defined [:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like set
[:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):] is Relation-like set
bool [:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):] is non empty set
n2 is set
n1 is set
n2 is set
[n1,n2] is V15() set
{n1,n2} is set
{n1} is set
{{n1,n2},{n1}} is set
<^p1,p2^> is set
<^o2,p1^> is set
<^o2,p2^> is set
{|o1|} . (o2,p1,p2) is set
o1 . (o2,p2) is set
o1 . [o2,p2] is set
n is Relation-like [:(o1 . (p1,p2)),(o1 . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like quasi_total M2( bool [:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):])
proj2 n is set
n2 is set
proj1 n is Relation-like set
n1 is set
n . n1 is set
n2 is set
n1 is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
<^p2,n^> is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
<^n,p2^> is set
the Arrows of C . (n,p2) is set
[n,p2] is V15() set
{n,p2} is set
{n} is set
{{n,p2},{n}} is set
the Arrows of C . [n,p2] is set
qq is M2(<^p2,n^>)
r1 is M2( the carrier of C)
r2 is M2( the carrier of C)
<^r1,r2^> is set
the Arrows of C . (r1,r2) is set
[r1,r2] is V15() set
{r1,r2} is set
{r1} is set
{{r1,r2},{r1}} is set
the Arrows of C . [r1,r2] is set
<^r2,r1^> is set
the Arrows of C . (r2,r1) is set
[r2,r1] is V15() set
{r2,r1} is set
{r2} is set
{{r2,r1},{r2}} is set
the Arrows of C . [r2,r1] is set
rr is M2(<^r1,r2^>)
<^r2,n^> is set
the Arrows of C . (r2,n) is set
[r2,n] is V15() set
{r2,n} is set
{{r2,n},{r2}} is set
the Arrows of C . [r2,n] is set
<^r1,n^> is set
the Arrows of C . (r1,n) is set
[r1,n] is V15() set
{r1,n} is set
{{r1,n},{r1}} is set
the Arrows of C . [r1,n] is set
<^n,r1^> is set
the Arrows of C . (n,r1) is set
[n,r1] is V15() set
{n,r1} is set
{{n,r1},{n}} is set
the Arrows of C . [n,r1] is set
mm is M2(<^r2,n^>)
mm * rr is M2(<^r1,n^>)
( the Comp of C . (o2,p1,p2)) . (mm,rr) is set
[mm,rr] is V15() set
{mm,rr} is set
{mm} is set
{{mm,rr},{mm}} is set
( the Comp of C . (o2,p1,p2)) . [mm,rr] is set
mm is M2( the carrier of C)
c₂₁ is M2( the carrier of C)
<^mm,c₂₁^> is set
the Arrows of C . (mm,c₂₁) is set
[mm,c₂₁] is V15() set
{mm,c₂₁} is set
{mm} is set
{{mm,c₂₁},{mm}} is set
the Arrows of C . [mm,c₂₁] is set
<^c₂₁,mm^> is set
the Arrows of C . (c₂₁,mm) is set
[c₂₁,mm] is V15() set
{c₂₁,mm} is set
{c₂₁} is set
{{c₂₁,mm},{c₂₁}} is set
the Arrows of C . [c₂₁,mm] is set
c₂₂ is M2(<^mm,c₂₁^>)
{|o1,o1|} . (o2,p1,p2) is set
o1 is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {|o1,o1|},{|o1|}
AltCatStr(# the carrier of C,o1,o1 #) is non empty strict AltCatStr
the carrier of AltCatStr(# the carrier of C,o1,o1 #) is non empty set
[: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] is Relation-like non empty set
the Arrows of AltCatStr(# the carrier of C,o1,o1 #) is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
[: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] is non empty set
the Comp of AltCatStr(# the carrier of C,o1,o1 #) is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) V36() V37() ManySortedFunction of {| the Arrows of AltCatStr(# the carrier of C,o1,o1 #), the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|},{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|}
{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #), the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|} is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|} is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
p2 is set
the Comp of AltCatStr(# the carrier of C,o1,o1 #) . p2 is Relation-like Function-like set
the Comp of C . p2 is Relation-like Function-like set
o1 . p2 is Relation-like Function-like set
n is M2( the carrier of C)
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
[n,n2,n1] is V15() V16() set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
[[n,n2],n1] is V15() set
{[n,n2],n1} is set
{[n,n2]} is Relation-like Function-like set
{{[n,n2],n1},{[n,n2]}} is set
the Comp of C . (n,n2,n1) is Relation-like [:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] -defined the Arrows of C . (n,n1) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):])
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
the Arrows of C . (n,n2) is set
the Arrows of C . [n,n2] is set
[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] is Relation-like set
the Arrows of C . (n,n1) is set
[n,n1] is V15() set
{n,n1} is set
{{n,n1},{n}} is set
the Arrows of C . [n,n1] is set
[:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):] is Relation-like set
bool [:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):] is non empty set
o1 . (n2,n1) is set
o1 . [n2,n1] is set
o1 . (n,n2) is set
o1 . [n,n2] is set
[:(o1 . (n2,n1)),(o1 . (n,n2)):] is Relation-like set
( the Comp of C . (n,n2,n1)) | [:(o1 . (n2,n1)),(o1 . (n,n2)):] is Relation-like [:(o1 . (n2,n1)),(o1 . (n,n2)):] -defined [:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] -defined the Arrows of C . (n,n1) -valued Function-like set
n2 is set
p2 is non empty strict SubCatStr of C
the carrier of p2 is non empty set
n is M2( the carrier of p2)
n2 is M2( the carrier of p2)
<^n,n2^> is set
the Arrows of p2 is Relation-like [: the carrier of p2, the carrier of p2:] -defined Function-like non empty V14([: the carrier of p2, the carrier of p2:]) set
[: the carrier of p2, the carrier of p2:] is Relation-like non empty set
the Arrows of p2 . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of p2 . [n,n2] is set
n1 is M2( the carrier of p2)
<^n2,n1^> is set
the Arrows of p2 . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of p2 . [n2,n1] is set
<^n,n1^> is set
the Arrows of p2 . (n,n1) is set
[n,n1] is V15() set
{n,n1} is set
{{n,n1},{n}} is set
the Arrows of p2 . [n,n1] is set
n2 is set
n1 is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
<^p2,n^> is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
<^n,p2^> is set
the Arrows of C . (n,p2) is set
[n,p2] is V15() set
{n,p2} is set
{n} is set
{{n,p2},{n}} is set
the Arrows of C . [n,p2] is set
qq is M2(<^p2,n^>)
r1 is M2( the carrier of C)
r2 is M2( the carrier of C)
<^r1,r2^> is set
the Arrows of C . (r1,r2) is set
[r1,r2] is V15() set
{r1,r2} is set
{r1} is set
{{r1,r2},{r1}} is set
the Arrows of C . [r1,r2] is set
<^r2,r1^> is set
the Arrows of C . (r2,r1) is set
[r2,r1] is V15() set
{r2,r1} is set
{r2} is set
{{r2,r1},{r2}} is set
the Arrows of C . [r2,r1] is set
rr is M2(<^r1,r2^>)
<^r2,n^> is set
the Arrows of C . (r2,n) is set
[r2,n] is V15() set
{r2,n} is set
{{r2,n},{r2}} is set
the Arrows of C . [r2,n] is set
mm is M2(<^r2,n^>)
mm * rr is M2(<^r1,n^>)
<^r1,n^> is set
the Arrows of C . (r1,n) is set
[r1,n] is V15() set
{r1,n} is set
{{r1,n},{r1}} is set
the Arrows of C . [r1,n] is set
<^n,r1^> is set
the Arrows of C . (n,r1) is set
[n,r1] is V15() set
{n,r1} is set
{{n,r1},{n}} is set
the Arrows of C . [n,r1] is set
c₂₁ is M2( the carrier of C)
c₂₂ is M2( the carrier of C)
<^c₂₁,c₂₂^> is set
the Arrows of C . (c₂₁,c₂₂) is set
[c₂₁,c₂₂] is V15() set
{c₂₁,c₂₂} is set
{c₂₁} is set
{{c₂₁,c₂₂},{c₂₁}} is set
the Arrows of C . [c₂₁,c₂₂] is set
<^c₂₂,c₂₁^> is set
the Arrows of C . (c₂₂,c₂₁) is set
[c₂₂,c₂₁] is V15() set
{c₂₂,c₂₁} is set
{c₂₂} is set
{{c₂₂,c₂₁},{c₂₂}} is set
the Arrows of C . [c₂₂,c₂₁] is set
c₂₃ is M2(<^c₂₁,c₂₂^>)
n is non empty transitive strict V129() SubCatStr of C
the carrier of n is non empty set
[: the carrier of n, the carrier of n:] is Relation-like non empty set
the Arrows of n is Relation-like [: the carrier of n, the carrier of n:] -defined Function-like non empty V14([: the carrier of n, the carrier of n:]) set
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
<^n2,n1^> is set
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
the Arrows of n . (n2,n1) is set
the Arrows of n . [n2,n1] is set
<^n1,n2^> is set
the Arrows of C . (n1,n2) is set
[n1,n2] is V15() set
{n1,n2} is set
{n1} is set
{{n1,n2},{n1}} is set
the Arrows of C . [n1,n2] is set
n2 is M2(<^n2,n1^>)
n1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^n1,p2^> is set
the Arrows of C . (n1,p2) is set
[n1,p2] is V15() set
{n1,p2} is set
{n1} is set
{{n1,p2},{n1}} is set
the Arrows of C . [n1,p2] is set
<^p2,n1^> is set
the Arrows of C . (p2,n1) is set
[p2,n1] is V15() set
{p2,n1} is set
{p2} is set
{{p2,n1},{p2}} is set
the Arrows of C . [p2,n1] is set
n is M2(<^n1,p2^>)
i is non empty transitive strict V129() SubCatStr of C
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
o1 is non empty transitive strict V129() SubCatStr of C
the carrier of o1 is non empty set
[: the carrier of o1, the carrier of o1:] is Relation-like non empty set
the Arrows of o1 is Relation-like [: the carrier of o1, the carrier of o1:] -defined Function-like non empty V14([: the carrier of o1, the carrier of o1:]) set
o2 is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of i . o2 is set
the Arrows of o1 . o2 is set
n is set
the Arrows of C . o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^p1,p2^>)
the Arrows of i . (p1,p2) is set
the Arrows of i . [p1,p2] is set
<^p2,p1^> is set
the Arrows of C . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of C . [p2,p1] is set
the Arrows of o1 . (p1,p2) is set
the Arrows of o1 . [p1,p2] is set
n is set
the Arrows of C . o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^p1,p2^>)
the Arrows of o1 . (p1,p2) is set
the Arrows of o1 . [p1,p2] is set
<^p2,p1^> is set
the Arrows of C . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of C . [p2,p1] is set
the Arrows of i . (p1,p2) is set
the Arrows of i . [p1,p2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() SubCatStr of C
the carrier of (C) is non empty set
the carrier of C is non empty set
i is M2( the carrier of (C))
o1 is M2( the carrier of C)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
<^i,i^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (i,i) is set
[i,i] is V15() set
{i,i} is set
{i} is set
{{i,i},{i}} is set
the Arrows of (C) . [i,i] is set
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
o1 is set
o2 is set
o1 is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
o2 is M2( the carrier of C)
p1 is M2( the carrier of C)
<^o2,p1^> is set
the Arrows of C . (o2,p1) is set
[o2,p1] is V15() set
{o2,p1} is set
{o2} is set
{{o2,p1},{o2}} is set
the Arrows of C . [o2,p1] is set
<^p1,o2^> is set
the Arrows of C . (p1,o2) is set
[p1,o2] is V15() set
{p1,o2} is set
{p1} is set
{{p1,o2},{p1}} is set
the Arrows of C . [p1,o2] is set
p2 is set
n is set
n2 is M2(<^o2,p1^>)
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
<^n2,n1^> is set
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
<^n1,n2^> is set
the Arrows of C . (n1,n2) is set
[n1,n2] is V15() set
{n1,n2} is set
{n1} is set
{{n1,n2},{n1}} is set
the Arrows of C . [n1,n2] is set
n2 is M2(<^n2,n1^>)
o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Comp of C is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {| the Arrows of C, the Arrows of C|},{| the Arrows of C|}
[: the carrier of C, the carrier of C, the carrier of C:] is non empty set
{| the Arrows of C, the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{| the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o2 is set
o1 is set
o2 is set
p1 is set
[o1,o2,p1] is V15() V16() set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
[[o1,o2],p1] is V15() set
{[o1,o2],p1} is set
{[o1,o2]} is Relation-like Function-like set
{{[o1,o2],p1},{[o1,o2]}} is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
n2 is M2( the carrier of C)
the Comp of C . (p2,n,n2) is Relation-like [:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] -defined the Arrows of C . (p2,n2) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):])
the Arrows of C . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of C . [n,n2] is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] is Relation-like set
the Arrows of C . (p2,n2) is set
[p2,n2] is V15() set
{p2,n2} is set
{{p2,n2},{p2}} is set
the Arrows of C . [p2,n2] is set
[:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):] is Relation-like set
bool [:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):] is non empty set
o1 . (n,n2) is set
o1 . [n,n2] is set
o1 . (p2,n) is set
o1 . [p2,n] is set
[:(o1 . (n,n2)),(o1 . (p2,n)):] is Relation-like set
( the Comp of C . (p2,n,n2)) | [:(o1 . (n,n2)),(o1 . (p2,n)):] is Relation-like [:(o1 . (n,n2)),(o1 . (p2,n)):] -defined [:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] -defined the Arrows of C . (p2,n2) -valued Function-like set
[p2,n,n2] is V15() V16() set
[[p2,n],n2] is V15() set
{[p2,n],n2} is set
{[p2,n]} is Relation-like Function-like set
{{[p2,n],n2},{[p2,n]}} is set
o2 is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o1 is set
o1 . o1 is set
the Arrows of C . o1 is set
o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
<^p2,p1^> is set
the Arrows of C . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of C . [p2,p1] is set
n is M2(<^p1,p2^>)
{|o1,o1|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{|o1|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o1 is set
o2 . o1 is set
{|o1,o1|} . o1 is set
{|o1|} . o1 is set
[:({|o1,o1|} . o1),({|o1|} . o1):] is Relation-like set
bool [:({|o1,o1|} . o1),({|o1|} . o1):] is non empty set
o2 is M2( the carrier of C)
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
[o2,p1,p2] is V15() V16() set
[o2,p1] is V15() set
{o2,p1} is set
{o2} is set
{{o2,p1},{o2}} is set
[[o2,p1],p2] is V15() set
{[o2,p1],p2} is set
{[o2,p1]} is Relation-like Function-like set
{{[o2,p1],p2},{[o2,p1]}} is set
the Comp of C . (o2,p1,p2) is Relation-like [:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):])
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
the Arrows of C . (o2,p1) is set
the Arrows of C . [o2,p1] is set
[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] is Relation-like set
the Arrows of C . (o2,p2) is set
[o2,p2] is V15() set
{o2,p2} is set
{{o2,p2},{o2}} is set
the Arrows of C . [o2,p2] is set
[:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):] is Relation-like set
bool [:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):] is non empty set
o1 . (p1,p2) is set
o1 . [p1,p2] is set
o1 . (o2,p1) is set
o1 . [o2,p1] is set
[:(o1 . (p1,p2)),(o1 . (o2,p1)):] is Relation-like set
( the Comp of C . (o2,p1,p2)) | [:(o1 . (p1,p2)),(o1 . (o2,p1)):] is Relation-like [:(o1 . (p1,p2)),(o1 . (o2,p1)):] -defined [:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like set
[:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):] is Relation-like set
bool [:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):] is non empty set
n2 is set
n1 is set
n2 is set
[n1,n2] is V15() set
{n1,n2} is set
{n1} is set
{{n1,n2},{n1}} is set
<^p1,p2^> is set
<^o2,p1^> is set
<^o2,p2^> is set
{|o1|} . (o2,p1,p2) is set
o1 . (o2,p2) is set
o1 . [o2,p2] is set
n is Relation-like [:(o1 . (p1,p2)),(o1 . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like quasi_total M2( bool [:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):])
proj2 n is set
n2 is set
proj1 n is Relation-like set
n1 is set
n . n1 is set
n2 is set
n1 is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
<^p2,n^> is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
<^n,p2^> is set
the Arrows of C . (n,p2) is set
[n,p2] is V15() set
{n,p2} is set
{n} is set
{{n,p2},{n}} is set
the Arrows of C . [n,p2] is set
qq is M2(<^p2,n^>)
r1 is M2( the carrier of C)
r2 is M2( the carrier of C)
<^r1,r2^> is set
the Arrows of C . (r1,r2) is set
[r1,r2] is V15() set
{r1,r2} is set
{r1} is set
{{r1,r2},{r1}} is set
the Arrows of C . [r1,r2] is set
<^r2,r1^> is set
the Arrows of C . (r2,r1) is set
[r2,r1] is V15() set
{r2,r1} is set
{r2} is set
{{r2,r1},{r2}} is set
the Arrows of C . [r2,r1] is set
rr is M2(<^r1,r2^>)
<^r2,n^> is set
the Arrows of C . (r2,n) is set
[r2,n] is V15() set
{r2,n} is set
{{r2,n},{r2}} is set
the Arrows of C . [r2,n] is set
<^r1,n^> is set
the Arrows of C . (r1,n) is set
[r1,n] is V15() set
{r1,n} is set
{{r1,n},{r1}} is set
the Arrows of C . [r1,n] is set
<^n,r1^> is set
the Arrows of C . (n,r1) is set
[n,r1] is V15() set
{n,r1} is set
{{n,r1},{n}} is set
the Arrows of C . [n,r1] is set
mm is M2(<^r2,n^>)
mm * rr is M2(<^r1,n^>)
( the Comp of C . (o2,p1,p2)) . (mm,rr) is set
[mm,rr] is V15() set
{mm,rr} is set
{mm} is set
{{mm,rr},{mm}} is set
( the Comp of C . (o2,p1,p2)) . [mm,rr] is set
mm is M2( the carrier of C)
c₂₁ is M2( the carrier of C)
<^mm,c₂₁^> is set
the Arrows of C . (mm,c₂₁) is set
[mm,c₂₁] is V15() set
{mm,c₂₁} is set
{mm} is set
{{mm,c₂₁},{mm}} is set
the Arrows of C . [mm,c₂₁] is set
<^c₂₁,mm^> is set
the Arrows of C . (c₂₁,mm) is set
[c₂₁,mm] is V15() set
{c₂₁,mm} is set
{c₂₁} is set
{{c₂₁,mm},{c₂₁}} is set
the Arrows of C . [c₂₁,mm] is set
c₂₂ is M2(<^mm,c₂₁^>)
{|o1,o1|} . (o2,p1,p2) is set
o1 is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {|o1,o1|},{|o1|}
AltCatStr(# the carrier of C,o1,o1 #) is non empty strict AltCatStr
the carrier of AltCatStr(# the carrier of C,o1,o1 #) is non empty set
[: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] is Relation-like non empty set
the Arrows of AltCatStr(# the carrier of C,o1,o1 #) is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
[: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] is non empty set
the Comp of AltCatStr(# the carrier of C,o1,o1 #) is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) V36() V37() ManySortedFunction of {| the Arrows of AltCatStr(# the carrier of C,o1,o1 #), the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|},{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|}
{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #), the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|} is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|} is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
p2 is set
the Comp of AltCatStr(# the carrier of C,o1,o1 #) . p2 is Relation-like Function-like set
the Comp of C . p2 is Relation-like Function-like set
o1 . p2 is Relation-like Function-like set
n is M2( the carrier of C)
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
[n,n2,n1] is V15() V16() set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
[[n,n2],n1] is V15() set
{[n,n2],n1} is set
{[n,n2]} is Relation-like Function-like set
{{[n,n2],n1},{[n,n2]}} is set
the Comp of C . (n,n2,n1) is Relation-like [:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] -defined the Arrows of C . (n,n1) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):])
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
the Arrows of C . (n,n2) is set
the Arrows of C . [n,n2] is set
[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] is Relation-like set
the Arrows of C . (n,n1) is set
[n,n1] is V15() set
{n,n1} is set
{{n,n1},{n}} is set
the Arrows of C . [n,n1] is set
[:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):] is Relation-like set
bool [:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):] is non empty set
o1 . (n2,n1) is set
o1 . [n2,n1] is set
o1 . (n,n2) is set
o1 . [n,n2] is set
[:(o1 . (n2,n1)),(o1 . (n,n2)):] is Relation-like set
( the Comp of C . (n,n2,n1)) | [:(o1 . (n2,n1)),(o1 . (n,n2)):] is Relation-like [:(o1 . (n2,n1)),(o1 . (n,n2)):] -defined [:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] -defined the Arrows of C . (n,n1) -valued Function-like set
n2 is set
p2 is non empty strict SubCatStr of C
the carrier of p2 is non empty set
n is M2( the carrier of p2)
n2 is M2( the carrier of p2)
<^n,n2^> is set
the Arrows of p2 is Relation-like [: the carrier of p2, the carrier of p2:] -defined Function-like non empty V14([: the carrier of p2, the carrier of p2:]) set
[: the carrier of p2, the carrier of p2:] is Relation-like non empty set
the Arrows of p2 . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of p2 . [n,n2] is set
n1 is M2( the carrier of p2)
<^n2,n1^> is set
the Arrows of p2 . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of p2 . [n2,n1] is set
<^n,n1^> is set
the Arrows of p2 . (n,n1) is set
[n,n1] is V15() set
{n,n1} is set
{{n,n1},{n}} is set
the Arrows of p2 . [n,n1] is set
n2 is set
n1 is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
<^p2,n^> is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
<^n,p2^> is set
the Arrows of C . (n,p2) is set
[n,p2] is V15() set
{n,p2} is set
{n} is set
{{n,p2},{n}} is set
the Arrows of C . [n,p2] is set
qq is M2(<^p2,n^>)
r1 is M2( the carrier of C)
r2 is M2( the carrier of C)
<^r1,r2^> is set
the Arrows of C . (r1,r2) is set
[r1,r2] is V15() set
{r1,r2} is set
{r1} is set
{{r1,r2},{r1}} is set
the Arrows of C . [r1,r2] is set
<^r2,r1^> is set
the Arrows of C . (r2,r1) is set
[r2,r1] is V15() set
{r2,r1} is set
{r2} is set
{{r2,r1},{r2}} is set
the Arrows of C . [r2,r1] is set
rr is M2(<^r1,r2^>)
<^r2,n^> is set
the Arrows of C . (r2,n) is set
[r2,n] is V15() set
{r2,n} is set
{{r2,n},{r2}} is set
the Arrows of C . [r2,n] is set
mm is M2(<^r2,n^>)
mm * rr is M2(<^r1,n^>)
<^r1,n^> is set
the Arrows of C . (r1,n) is set
[r1,n] is V15() set
{r1,n} is set
{{r1,n},{r1}} is set
the Arrows of C . [r1,n] is set
<^n,r1^> is set
the Arrows of C . (n,r1) is set
[n,r1] is V15() set
{n,r1} is set
{{n,r1},{n}} is set
the Arrows of C . [n,r1] is set
c₂₁ is M2( the carrier of C)
c₂₂ is M2( the carrier of C)
<^c₂₁,c₂₂^> is set
the Arrows of C . (c₂₁,c₂₂) is set
[c₂₁,c₂₂] is V15() set
{c₂₁,c₂₂} is set
{c₂₁} is set
{{c₂₁,c₂₂},{c₂₁}} is set
the Arrows of C . [c₂₁,c₂₂] is set
<^c₂₂,c₂₁^> is set
the Arrows of C . (c₂₂,c₂₁) is set
[c₂₂,c₂₁] is V15() set
{c₂₂,c₂₁} is set
{c₂₂} is set
{{c₂₂,c₂₁},{c₂₂}} is set
the Arrows of C . [c₂₂,c₂₁] is set
c₂₃ is M2(<^c₂₁,c₂₂^>)
n is non empty transitive strict V129() SubCatStr of C
the carrier of n is non empty set
[: the carrier of n, the carrier of n:] is Relation-like non empty set
the Arrows of n is Relation-like [: the carrier of n, the carrier of n:] -defined Function-like non empty V14([: the carrier of n, the carrier of n:]) set
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
<^n2,n1^> is set
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
the Arrows of n . (n2,n1) is set
the Arrows of n . [n2,n1] is set
<^n1,n2^> is set
the Arrows of C . (n1,n2) is set
[n1,n2] is V15() set
{n1,n2} is set
{n1} is set
{{n1,n2},{n1}} is set
the Arrows of C . [n1,n2] is set
n2 is M2(<^n2,n1^>)
n1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^n1,p2^> is set
the Arrows of C . (n1,p2) is set
[n1,p2] is V15() set
{n1,p2} is set
{n1} is set
{{n1,p2},{n1}} is set
the Arrows of C . [n1,p2] is set
<^p2,n1^> is set
the Arrows of C . (p2,n1) is set
[p2,n1] is V15() set
{p2,n1} is set
{p2} is set
{{p2,n1},{p2}} is set
the Arrows of C . [p2,n1] is set
n is M2(<^n1,p2^>)
i is non empty transitive strict V129() SubCatStr of C
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
o1 is non empty transitive strict V129() SubCatStr of C
the carrier of o1 is non empty set
[: the carrier of o1, the carrier of o1:] is Relation-like non empty set
the Arrows of o1 is Relation-like [: the carrier of o1, the carrier of o1:] -defined Function-like non empty V14([: the carrier of o1, the carrier of o1:]) set
o2 is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of i . o2 is set
the Arrows of o1 . o2 is set
n is set
the Arrows of C . o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^p1,p2^>)
the Arrows of i . (p1,p2) is set
the Arrows of i . [p1,p2] is set
<^p2,p1^> is set
the Arrows of C . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of C . [p2,p1] is set
the Arrows of o1 . (p1,p2) is set
the Arrows of o1 . [p1,p2] is set
n is set
the Arrows of C . o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^p1,p2^>)
the Arrows of o1 . (p1,p2) is set
the Arrows of o1 . [p1,p2] is set
<^p2,p1^> is set
the Arrows of C . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of C . [p2,p1] is set
the Arrows of i . (p1,p2) is set
the Arrows of i . [p1,p2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() SubCatStr of C
the carrier of (C) is non empty set
the carrier of C is non empty set
i is M2( the carrier of (C))
o1 is M2( the carrier of C)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
<^i,i^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (i,i) is set
[i,i] is V15() set
{i,i} is set
{i} is set
{{i,i},{i}} is set
the Arrows of (C) . [i,i] is set
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
o1 is set
o2 is set
o1 is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
o2 is M2( the carrier of C)
p1 is M2( the carrier of C)
<^o2,p1^> is set
the Arrows of C . (o2,p1) is set
[o2,p1] is V15() set
{o2,p1} is set
{o2} is set
{{o2,p1},{o2}} is set
the Arrows of C . [o2,p1] is set
<^p1,o2^> is set
the Arrows of C . (p1,o2) is set
[p1,o2] is V15() set
{p1,o2} is set
{p1} is set
{{p1,o2},{p1}} is set
the Arrows of C . [p1,o2] is set
p2 is set
n is set
n2 is M2(<^o2,p1^>)
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
<^n2,n1^> is set
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
<^n1,n2^> is set
the Arrows of C . (n1,n2) is set
[n1,n2] is V15() set
{n1,n2} is set
{n1} is set
{{n1,n2},{n1}} is set
the Arrows of C . [n1,n2] is set
n2 is M2(<^n2,n1^>)
o1 is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Comp of C is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {| the Arrows of C, the Arrows of C|},{| the Arrows of C|}
[: the carrier of C, the carrier of C, the carrier of C:] is non empty set
{| the Arrows of C, the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{| the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o2 is set
o1 is set
o2 is set
p1 is set
[o1,o2,p1] is V15() V16() set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
[[o1,o2],p1] is V15() set
{[o1,o2],p1} is set
{[o1,o2]} is Relation-like Function-like set
{{[o1,o2],p1},{[o1,o2]}} is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
n2 is M2( the carrier of C)
the Comp of C . (p2,n,n2) is Relation-like [:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] -defined the Arrows of C . (p2,n2) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):])
the Arrows of C . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of C . [n,n2] is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] is Relation-like set
the Arrows of C . (p2,n2) is set
[p2,n2] is V15() set
{p2,n2} is set
{{p2,n2},{p2}} is set
the Arrows of C . [p2,n2] is set
[:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):] is Relation-like set
bool [:[:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):],( the Arrows of C . (p2,n2)):] is non empty set
o1 . (n,n2) is set
o1 . [n,n2] is set
o1 . (p2,n) is set
o1 . [p2,n] is set
[:(o1 . (n,n2)),(o1 . (p2,n)):] is Relation-like set
( the Comp of C . (p2,n,n2)) | [:(o1 . (n,n2)),(o1 . (p2,n)):] is Relation-like [:(o1 . (n,n2)),(o1 . (p2,n)):] -defined [:( the Arrows of C . (n,n2)),( the Arrows of C . (p2,n)):] -defined the Arrows of C . (p2,n2) -valued Function-like set
[p2,n,n2] is V15() V16() set
[[p2,n],n2] is V15() set
{[p2,n],n2} is set
{[p2,n]} is Relation-like Function-like set
{{[p2,n],n2},{[p2,n]}} is set
o2 is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o1 is set
o1 . o1 is set
the Arrows of C . o1 is set
o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
<^p2,p1^> is set
the Arrows of C . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of C . [p2,p1] is set
n is M2(<^p1,p2^>)
{|o1,o1|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{|o1|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
o1 is set
o2 . o1 is set
{|o1,o1|} . o1 is set
{|o1|} . o1 is set
[:({|o1,o1|} . o1),({|o1|} . o1):] is Relation-like set
bool [:({|o1,o1|} . o1),({|o1|} . o1):] is non empty set
o2 is M2( the carrier of C)
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
[o2,p1,p2] is V15() V16() set
[o2,p1] is V15() set
{o2,p1} is set
{o2} is set
{{o2,p1},{o2}} is set
[[o2,p1],p2] is V15() set
{[o2,p1],p2} is set
{[o2,p1]} is Relation-like Function-like set
{{[o2,p1],p2},{[o2,p1]}} is set
the Comp of C . (o2,p1,p2) is Relation-like [:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):])
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
the Arrows of C . (o2,p1) is set
the Arrows of C . [o2,p1] is set
[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] is Relation-like set
the Arrows of C . (o2,p2) is set
[o2,p2] is V15() set
{o2,p2} is set
{{o2,p2},{o2}} is set
the Arrows of C . [o2,p2] is set
[:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):] is Relation-like set
bool [:[:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):],( the Arrows of C . (o2,p2)):] is non empty set
o1 . (p1,p2) is set
o1 . [p1,p2] is set
o1 . (o2,p1) is set
o1 . [o2,p1] is set
[:(o1 . (p1,p2)),(o1 . (o2,p1)):] is Relation-like set
( the Comp of C . (o2,p1,p2)) | [:(o1 . (p1,p2)),(o1 . (o2,p1)):] is Relation-like [:(o1 . (p1,p2)),(o1 . (o2,p1)):] -defined [:( the Arrows of C . (p1,p2)),( the Arrows of C . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like set
[:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):] is Relation-like set
bool [:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):] is non empty set
n2 is set
n1 is set
n2 is set
[n1,n2] is V15() set
{n1,n2} is set
{n1} is set
{{n1,n2},{n1}} is set
<^p1,p2^> is set
<^o2,p1^> is set
<^o2,p2^> is set
{|o1|} . (o2,p1,p2) is set
o1 . (o2,p2) is set
o1 . [o2,p2] is set
n is Relation-like [:(o1 . (p1,p2)),(o1 . (o2,p1)):] -defined the Arrows of C . (o2,p2) -valued Function-like quasi_total M2( bool [:[:(o1 . (p1,p2)),(o1 . (o2,p1)):],( the Arrows of C . (o2,p2)):])
proj2 n is set
n2 is set
proj1 n is Relation-like set
n1 is set
n . n1 is set
n2 is set
n1 is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
<^p2,n^> is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
<^n,p2^> is set
the Arrows of C . (n,p2) is set
[n,p2] is V15() set
{n,p2} is set
{n} is set
{{n,p2},{n}} is set
the Arrows of C . [n,p2] is set
qq is M2(<^p2,n^>)
r1 is M2( the carrier of C)
r2 is M2( the carrier of C)
<^r1,r2^> is set
the Arrows of C . (r1,r2) is set
[r1,r2] is V15() set
{r1,r2} is set
{r1} is set
{{r1,r2},{r1}} is set
the Arrows of C . [r1,r2] is set
<^r2,r1^> is set
the Arrows of C . (r2,r1) is set
[r2,r1] is V15() set
{r2,r1} is set
{r2} is set
{{r2,r1},{r2}} is set
the Arrows of C . [r2,r1] is set
rr is M2(<^r1,r2^>)
<^r2,n^> is set
the Arrows of C . (r2,n) is set
[r2,n] is V15() set
{r2,n} is set
{{r2,n},{r2}} is set
the Arrows of C . [r2,n] is set
<^r1,n^> is set
the Arrows of C . (r1,n) is set
[r1,n] is V15() set
{r1,n} is set
{{r1,n},{r1}} is set
the Arrows of C . [r1,n] is set
<^n,r1^> is set
the Arrows of C . (n,r1) is set
[n,r1] is V15() set
{n,r1} is set
{{n,r1},{n}} is set
the Arrows of C . [n,r1] is set
mm is M2(<^r2,n^>)
mm * rr is M2(<^r1,n^>)
( the Comp of C . (o2,p1,p2)) . (mm,rr) is set
[mm,rr] is V15() set
{mm,rr} is set
{mm} is set
{{mm,rr},{mm}} is set
( the Comp of C . (o2,p1,p2)) . [mm,rr] is set
mm is M2( the carrier of C)
c₂₁ is M2( the carrier of C)
<^mm,c₂₁^> is set
the Arrows of C . (mm,c₂₁) is set
[mm,c₂₁] is V15() set
{mm,c₂₁} is set
{mm} is set
{{mm,c₂₁},{mm}} is set
the Arrows of C . [mm,c₂₁] is set
<^c₂₁,mm^> is set
the Arrows of C . (c₂₁,mm) is set
[c₂₁,mm] is V15() set
{c₂₁,mm} is set
{c₂₁} is set
{{c₂₁,mm},{c₂₁}} is set
the Arrows of C . [c₂₁,mm] is set
c₂₂ is M2(<^mm,c₂₁^>)
{|o1,o1|} . (o2,p1,p2) is set
o1 is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {|o1,o1|},{|o1|}
AltCatStr(# the carrier of C,o1,o1 #) is non empty strict AltCatStr
the carrier of AltCatStr(# the carrier of C,o1,o1 #) is non empty set
[: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] is Relation-like non empty set
the Arrows of AltCatStr(# the carrier of C,o1,o1 #) is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
[: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] is non empty set
the Comp of AltCatStr(# the carrier of C,o1,o1 #) is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) V36() V37() ManySortedFunction of {| the Arrows of AltCatStr(# the carrier of C,o1,o1 #), the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|},{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|}
{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #), the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|} is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
{| the Arrows of AltCatStr(# the carrier of C,o1,o1 #)|} is Relation-like [: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #), the carrier of AltCatStr(# the carrier of C,o1,o1 #):]) set
p2 is set
the Comp of AltCatStr(# the carrier of C,o1,o1 #) . p2 is Relation-like Function-like set
the Comp of C . p2 is Relation-like Function-like set
o1 . p2 is Relation-like Function-like set
n is M2( the carrier of C)
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
[n,n2,n1] is V15() V16() set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
[[n,n2],n1] is V15() set
{[n,n2],n1} is set
{[n,n2]} is Relation-like Function-like set
{{[n,n2],n1},{[n,n2]}} is set
the Comp of C . (n,n2,n1) is Relation-like [:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] -defined the Arrows of C . (n,n1) -valued Function-like quasi_total M2( bool [:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):])
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
the Arrows of C . (n,n2) is set
the Arrows of C . [n,n2] is set
[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] is Relation-like set
the Arrows of C . (n,n1) is set
[n,n1] is V15() set
{n,n1} is set
{{n,n1},{n}} is set
the Arrows of C . [n,n1] is set
[:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):] is Relation-like set
bool [:[:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):],( the Arrows of C . (n,n1)):] is non empty set
o1 . (n2,n1) is set
o1 . [n2,n1] is set
o1 . (n,n2) is set
o1 . [n,n2] is set
[:(o1 . (n2,n1)),(o1 . (n,n2)):] is Relation-like set
( the Comp of C . (n,n2,n1)) | [:(o1 . (n2,n1)),(o1 . (n,n2)):] is Relation-like [:(o1 . (n2,n1)),(o1 . (n,n2)):] -defined [:( the Arrows of C . (n2,n1)),( the Arrows of C . (n,n2)):] -defined the Arrows of C . (n,n1) -valued Function-like set
n2 is set
p2 is non empty strict SubCatStr of C
the carrier of p2 is non empty set
n is M2( the carrier of p2)
n2 is M2( the carrier of p2)
<^n,n2^> is set
the Arrows of p2 is Relation-like [: the carrier of p2, the carrier of p2:] -defined Function-like non empty V14([: the carrier of p2, the carrier of p2:]) set
[: the carrier of p2, the carrier of p2:] is Relation-like non empty set
the Arrows of p2 . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of p2 . [n,n2] is set
n1 is M2( the carrier of p2)
<^n2,n1^> is set
the Arrows of p2 . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of p2 . [n2,n1] is set
<^n,n1^> is set
the Arrows of p2 . (n,n1) is set
[n,n1] is V15() set
{n,n1} is set
{{n,n1},{n}} is set
the Arrows of p2 . [n,n1] is set
n2 is set
n1 is set
p2 is M2( the carrier of C)
n is M2( the carrier of C)
<^p2,n^> is set
the Arrows of C . (p2,n) is set
[p2,n] is V15() set
{p2,n} is set
{p2} is set
{{p2,n},{p2}} is set
the Arrows of C . [p2,n] is set
<^n,p2^> is set
the Arrows of C . (n,p2) is set
[n,p2] is V15() set
{n,p2} is set
{n} is set
{{n,p2},{n}} is set
the Arrows of C . [n,p2] is set
qq is M2(<^p2,n^>)
r1 is M2( the carrier of C)
r2 is M2( the carrier of C)
<^r1,r2^> is set
the Arrows of C . (r1,r2) is set
[r1,r2] is V15() set
{r1,r2} is set
{r1} is set
{{r1,r2},{r1}} is set
the Arrows of C . [r1,r2] is set
<^r2,r1^> is set
the Arrows of C . (r2,r1) is set
[r2,r1] is V15() set
{r2,r1} is set
{r2} is set
{{r2,r1},{r2}} is set
the Arrows of C . [r2,r1] is set
rr is M2(<^r1,r2^>)
<^r2,n^> is set
the Arrows of C . (r2,n) is set
[r2,n] is V15() set
{r2,n} is set
{{r2,n},{r2}} is set
the Arrows of C . [r2,n] is set
mm is M2(<^r2,n^>)
mm * rr is M2(<^r1,n^>)
<^r1,n^> is set
the Arrows of C . (r1,n) is set
[r1,n] is V15() set
{r1,n} is set
{{r1,n},{r1}} is set
the Arrows of C . [r1,n] is set
<^n,r1^> is set
the Arrows of C . (n,r1) is set
[n,r1] is V15() set
{n,r1} is set
{{n,r1},{n}} is set
the Arrows of C . [n,r1] is set
c₂₁ is M2( the carrier of C)
c₂₂ is M2( the carrier of C)
<^c₂₁,c₂₂^> is set
the Arrows of C . (c₂₁,c₂₂) is set
[c₂₁,c₂₂] is V15() set
{c₂₁,c₂₂} is set
{c₂₁} is set
{{c₂₁,c₂₂},{c₂₁}} is set
the Arrows of C . [c₂₁,c₂₂] is set
<^c₂₂,c₂₁^> is set
the Arrows of C . (c₂₂,c₂₁) is set
[c₂₂,c₂₁] is V15() set
{c₂₂,c₂₁} is set
{c₂₂} is set
{{c₂₂,c₂₁},{c₂₂}} is set
the Arrows of C . [c₂₂,c₂₁] is set
c₂₃ is M2(<^c₂₁,c₂₂^>)
n is non empty transitive strict V129() SubCatStr of C
the carrier of n is non empty set
[: the carrier of n, the carrier of n:] is Relation-like non empty set
the Arrows of n is Relation-like [: the carrier of n, the carrier of n:] -defined Function-like non empty V14([: the carrier of n, the carrier of n:]) set
n2 is M2( the carrier of C)
n1 is M2( the carrier of C)
<^n2,n1^> is set
the Arrows of C . (n2,n1) is set
[n2,n1] is V15() set
{n2,n1} is set
{n2} is set
{{n2,n1},{n2}} is set
the Arrows of C . [n2,n1] is set
the Arrows of n . (n2,n1) is set
the Arrows of n . [n2,n1] is set
<^n1,n2^> is set
the Arrows of C . (n1,n2) is set
[n1,n2] is V15() set
{n1,n2} is set
{n1} is set
{{n1,n2},{n1}} is set
the Arrows of C . [n1,n2] is set
n2 is M2(<^n2,n1^>)
n1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^n1,p2^> is set
the Arrows of C . (n1,p2) is set
[n1,p2] is V15() set
{n1,p2} is set
{n1} is set
{{n1,p2},{n1}} is set
the Arrows of C . [n1,p2] is set
<^p2,n1^> is set
the Arrows of C . (p2,n1) is set
[p2,n1] is V15() set
{p2,n1} is set
{p2} is set
{{p2,n1},{p2}} is set
the Arrows of C . [p2,n1] is set
n is M2(<^n1,p2^>)
i is non empty transitive strict V129() SubCatStr of C
the carrier of i is non empty set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
o1 is non empty transitive strict V129() SubCatStr of C
the carrier of o1 is non empty set
[: the carrier of o1, the carrier of o1:] is Relation-like non empty set
the Arrows of o1 is Relation-like [: the carrier of o1, the carrier of o1:] -defined Function-like non empty V14([: the carrier of o1, the carrier of o1:]) set
o2 is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of i . o2 is set
the Arrows of o1 . o2 is set
n is set
the Arrows of C . o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^p1,p2^>)
the Arrows of i . (p1,p2) is set
the Arrows of i . [p1,p2] is set
<^p2,p1^> is set
the Arrows of C . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of C . [p2,p1] is set
the Arrows of o1 . (p1,p2) is set
the Arrows of o1 . [p1,p2] is set
n is set
the Arrows of C . o2 is set
p1 is M2( the carrier of C)
p2 is M2( the carrier of C)
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^p1,p2^>)
the Arrows of o1 . (p1,p2) is set
the Arrows of o1 . [p1,p2] is set
<^p2,p1^> is set
the Arrows of C . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of C . [p2,p1] is set
the Arrows of i . (p1,p2) is set
the Arrows of i . [p1,p2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() SubCatStr of C
the carrier of (C) is non empty set
the carrier of C is non empty set
i is M2( the carrier of (C))
o1 is M2( the carrier of C)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
<^i,i^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (i,i) is set
[i,i] is V15() set
{i,i} is set
{i} is set
{{i,i},{i}} is set
the Arrows of (C) . [i,i] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of (C) is non empty set
the carrier of C is non empty set
the carrier of (C) is non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
i is set
the Arrows of (C) . i is set
the Arrows of (C) . i is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
p1 is set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
the Arrows of C . (o1,o2) is set
the Arrows of C . [o1,o2] is set
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
p2 is M2(<^o1,o2^>)
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
the Arrows of (C) . (o1,o2) is set
the Arrows of (C) . [o1,o2] is set
i is non empty with_units reflexive SubCatStr of (C)
the carrier of i is non empty set
o1 is M2( the carrier of i)
o2 is M2( the carrier of (C))
idm o1 is retraction coretraction mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of i . [o1,o1] is set
o1 is M2( the carrier of C)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
idm o2 is retraction coretraction iso mono epi M2(<^o2,o2^>)
<^o2,o2^> is non empty set
the Arrows of (C) . (o2,o2) is set
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the Arrows of (C) . [o2,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of (C) is non empty set
the carrier of C is non empty set
the carrier of (C) is non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
i is set
the Arrows of (C) . i is set
the Arrows of (C) . i is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
p1 is set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
the Arrows of C . (o1,o2) is set
the Arrows of C . [o1,o2] is set
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
p2 is M2(<^o1,o2^>)
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
the Arrows of (C) . (o1,o2) is set
the Arrows of (C) . [o1,o2] is set
i is non empty with_units reflexive SubCatStr of (C)
the carrier of i is non empty set
o1 is M2( the carrier of i)
o2 is M2( the carrier of (C))
idm o1 is retraction coretraction mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of i . [o1,o1] is set
o1 is M2( the carrier of C)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
idm o2 is retraction coretraction iso mono epi M2(<^o2,o2^>)
<^o2,o2^> is non empty set
the Arrows of (C) . (o2,o2) is set
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the Arrows of (C) . [o2,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of (C) is non empty set
the carrier of C is non empty set
the carrier of (C) is non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
i is set
the Arrows of (C) . i is set
the Arrows of (C) . i is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
p1 is set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
the Arrows of C . (o1,o2) is set
the Arrows of C . [o1,o2] is set
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
p2 is M2(<^o1,o2^>)
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
the Arrows of (C) . (o1,o2) is set
the Arrows of (C) . [o1,o2] is set
i is non empty with_units reflexive SubCatStr of (C)
the carrier of i is non empty set
o1 is M2( the carrier of i)
o2 is M2( the carrier of (C))
idm o1 is retraction coretraction mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of i . [o1,o1] is set
o1 is M2( the carrier of C)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
idm o2 is retraction coretraction iso mono epi M2(<^o2,o2^>)
<^o2,o2^> is non empty set
the Arrows of (C) . (o2,o2) is set
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the Arrows of (C) . [o2,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of (C) is non empty set
the carrier of C is non empty set
the carrier of (C) is non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
i is set
the Arrows of (C) . i is set
the Arrows of (C) . i is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
p1 is set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
the Arrows of C . (o1,o2) is set
the Arrows of C . [o1,o2] is set
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
p2 is M2(<^o1,o2^>)
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
the Arrows of (C) . (o1,o2) is set
the Arrows of (C) . [o1,o2] is set
i is non empty with_units reflexive SubCatStr of (C)
the carrier of i is non empty set
o1 is M2( the carrier of i)
o2 is M2( the carrier of (C))
idm o1 is retraction coretraction mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of i is Relation-like [: the carrier of i, the carrier of i:] -defined Function-like non empty V14([: the carrier of i, the carrier of i:]) set
[: the carrier of i, the carrier of i:] is Relation-like non empty set
the Arrows of i . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of i . [o1,o1] is set
o1 is M2( the carrier of C)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
idm o2 is retraction coretraction iso mono epi M2(<^o2,o2^>)
<^o2,o2^> is non empty set
the Arrows of (C) . (o2,o2) is set
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the Arrows of (C) . [o2,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Comp of C is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {| the Arrows of C, the Arrows of C|},{| the Arrows of C|}
[: the carrier of C, the carrier of C, the carrier of C:] is non empty set
{| the Arrows of C, the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{| the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
AltCatStr(# the carrier of C, the Arrows of C, the Comp of C #) is non empty strict AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of (C) is non empty set
the carrier of AltCatStr(# the carrier of C, the Arrows of C, the Comp of C #) is non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
i is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . i is set
the Arrows of C . i is set
p1 is set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
p2 is M2(<^o1,o2^>)
the Arrows of (C) . (o1,o2) is set
the Arrows of (C) . [o1,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Comp of C is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {| the Arrows of C, the Arrows of C|},{| the Arrows of C|}
[: the carrier of C, the carrier of C, the carrier of C:] is non empty set
{| the Arrows of C, the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{| the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
AltCatStr(# the carrier of C, the Arrows of C, the Comp of C #) is non empty strict AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of (C) is non empty set
the carrier of AltCatStr(# the carrier of C, the Arrows of C, the Comp of C #) is non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
i is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . i is set
the Arrows of C . i is set
p1 is set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
p2 is M2(<^o1,o2^>)
the Arrows of (C) . (o1,o2) is set
the Arrows of (C) . [o1,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Comp of C is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {| the Arrows of C, the Arrows of C|},{| the Arrows of C|}
[: the carrier of C, the carrier of C, the carrier of C:] is non empty set
{| the Arrows of C, the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{| the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
AltCatStr(# the carrier of C, the Arrows of C, the Comp of C #) is non empty strict AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of (C) is non empty set
the carrier of AltCatStr(# the carrier of C, the Arrows of C, the Comp of C #) is non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
i is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . i is set
the Arrows of C . i is set
p1 is set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
p2 is M2(<^o1,o2^>)
the Arrows of (C) . (o1,o2) is set
the Arrows of (C) . [o1,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Comp of C is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {| the Arrows of C, the Arrows of C|},{| the Arrows of C|}
[: the carrier of C, the carrier of C, the carrier of C:] is non empty set
{| the Arrows of C, the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{| the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
AltCatStr(# the carrier of C, the Arrows of C, the Comp of C #) is non empty strict AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of (C) is non empty set
the carrier of AltCatStr(# the carrier of C, the Arrows of C, the Comp of C #) is non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
i is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . i is set
the Arrows of C . i is set
p1 is set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
p2 is M2(<^o1,o2^>)
the Arrows of (C) . (o1,o2) is set
the Arrows of (C) . [o1,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
the carrier of C is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Comp of C is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of {| the Arrows of C, the Arrows of C|},{| the Arrows of C|}
[: the carrier of C, the carrier of C, the carrier of C:] is non empty set
{| the Arrows of C, the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
{| the Arrows of C|} is Relation-like [: the carrier of C, the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C, the carrier of C:]) set
AltCatStr(# the carrier of C, the Arrows of C, the Comp of C #) is non empty strict AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of (C) is non empty set
the carrier of AltCatStr(# the carrier of C, the Arrows of C, the Comp of C #) is non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
i is set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . i is set
the Arrows of C . i is set
p1 is set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
<^o1,o2^> is set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
p2 is M2(<^o1,o2^>)
the Arrows of (C) . (o1,o2) is set
the Arrows of (C) . [o1,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of (C) is non empty set
i is M2( the carrier of (C))
o1 is M2( the carrier of (C))
<^i,o1^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{i} is set
{{i,o1},{i}} is set
the Arrows of (C) . [i,o1] is set
o2 is M2(<^i,o1^>)
the carrier of C is non empty set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
<^o1,o2^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
p1 is M2(<^o1,o2^>)
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of (C) is non empty set
i is M2( the carrier of (C))
o1 is M2( the carrier of (C))
<^i,o1^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{i} is set
{{i,o1},{i}} is set
the Arrows of (C) . [i,o1] is set
o2 is M2(<^i,o1^>)
the carrier of C is non empty set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
<^o1,o2^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
p1 is M2(<^o1,o2^>)
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of (C) is non empty set
i is M2( the carrier of (C))
o1 is M2( the carrier of (C))
<^i,o1^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (i,o1) is set
[i,o1] is V15() set
{i,o1} is set
{i} is set
{{i,o1},{i}} is set
the Arrows of (C) . [i,o1] is set
<^o1,i^> is set
the Arrows of (C) . (o1,i) is set
[o1,i] is V15() set
{o1,i} is set
{o1} is set
{{o1,i},{o1}} is set
the Arrows of (C) . [o1,i] is set
o2 is M2(<^i,o1^>)
o2 " is M2(<^o1,i^>)
the carrier of C is non empty set
o1 is M2( the carrier of C)
o2 is M2( the carrier of C)
<^o1,o2^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the Arrows of C . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of C . [o1,o2] is set
p1 is M2(<^o1,o2^>)
<^o2,o1^> is set
the Arrows of C . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of C . [o2,o1] is set
p1 " is M2(<^o2,o1^>)
the Arrows of (C) . (o2,o1) is set
the Arrows of (C) . [o2,o1] is set
p2 is M2(<^o1,i^>)
o2 * p2 is M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of (C) . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of (C) . [o1,o1] is set
p1 * (p1 ") is M2(<^o2,o2^>)
<^o2,o2^> is non empty set
the Arrows of C . (o2,o2) is set
[o2,o2] is V15() set
{o2,o2} is set
{{o2,o2},{o2}} is set
the Arrows of C . [o2,o2] is set
idm o2 is retraction coretraction iso mono epi M2(<^o2,o2^>)
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
p2 is M2(<^o1,i^>)
p2 * o2 is M2(<^i,i^>)
<^i,i^> is non empty set
the Arrows of (C) . (i,i) is set
[i,i] is V15() set
{i,i} is set
{{i,i},{i}} is set
the Arrows of (C) . [i,i] is set
(p1 ") * p1 is M2(<^o1,o1^>)
<^o1,o1^> is non empty set
the Arrows of C . (o1,o1) is set
[o1,o1] is V15() set
{o1,o1} is set
{{o1,o1},{o1}} is set
the Arrows of C . [o1,o1] is set
idm o1 is retraction coretraction iso mono epi M2(<^o1,o1^>)
idm i is retraction coretraction iso mono epi M2(<^i,i^>)
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
((C)) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of (C)
the carrier of ((C)) is non empty set
the carrier of (C) is non empty set
the carrier of C is non empty set
[: the carrier of ((C)), the carrier of ((C)):] is Relation-like non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of ((C)) is Relation-like [: the carrier of ((C)), the carrier of ((C)):] -defined Function-like non empty V14([: the carrier of ((C)), the carrier of ((C)):]) set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
i is set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of ((C)) . i is set
the Arrows of (C) . i is set
p1 is set
o1 is M2( the carrier of (C))
o2 is M2( the carrier of (C))
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
p2 is M2(<^o1,o2^>)
the Arrows of ((C)) . (o1,o2) is set
the Arrows of ((C)) . [o1,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
((C)) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of (C)
the carrier of ((C)) is non empty set
the carrier of (C) is non empty set
the carrier of C is non empty set
[: the carrier of ((C)), the carrier of ((C)):] is Relation-like non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of ((C)) is Relation-like [: the carrier of ((C)), the carrier of ((C)):] -defined Function-like non empty V14([: the carrier of ((C)), the carrier of ((C)):]) set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
i is set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of ((C)) . i is set
the Arrows of (C) . i is set
p1 is set
o1 is M2( the carrier of (C))
o2 is M2( the carrier of (C))
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
p2 is M2(<^o1,o2^>)
the Arrows of ((C)) . (o1,o2) is set
the Arrows of ((C)) . [o1,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
((C)) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of (C)
the carrier of ((C)) is non empty set
the carrier of (C) is non empty set
the carrier of C is non empty set
[: the carrier of ((C)), the carrier of ((C)):] is Relation-like non empty set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of ((C)) is Relation-like [: the carrier of ((C)), the carrier of ((C)):] -defined Function-like non empty V14([: the carrier of ((C)), the carrier of ((C)):]) set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
i is set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of ((C)) . i is set
the Arrows of (C) . i is set
p1 is set
o1 is M2( the carrier of (C))
o2 is M2( the carrier of (C))
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
p2 is M2(<^o1,o2^>)
p2 " is M2(<^o2,o1^>)
<^o2,o1^> is set
the Arrows of (C) . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of (C) . [o2,o1] is set
the Arrows of ((C)) . (o1,o2) is set
the Arrows of ((C)) . [o1,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
((C)) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of (C)
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of ((C)) is non empty set
the carrier of (C) is non empty set
the carrier of (C) is non empty set
the carrier of C is non empty set
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
i is set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of ((C)) is Relation-like [: the carrier of ((C)), the carrier of ((C)):] -defined Function-like non empty V14([: the carrier of ((C)), the carrier of ((C)):]) set
[: the carrier of ((C)), the carrier of ((C)):] is Relation-like non empty set
the Arrows of ((C)) . i is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . i is set
o1 is M2( the carrier of (C))
o2 is M2( the carrier of (C))
n2 is M2( the carrier of ((C)))
n is M2( the carrier of ((C)))
<^n2,n^> is set
the Arrows of ((C)) . (n2,n) is set
[n2,n] is V15() set
{n2,n} is set
{n2} is set
{{n2,n},{n2}} is set
the Arrows of ((C)) . [n2,n] is set
<^o2,o1^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of (C) . [o2,o1] is set
n1 is set
<^n,n2^> is set
the Arrows of ((C)) . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of ((C)) . [n,n2] is set
p2 is M2( the carrier of C)
p1 is M2( the carrier of C)
<^p2,p1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Arrows of C . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of C . [p2,p1] is set
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^o1,o2^>)
n1 is M2(<^p1,p2^>)
the Arrows of (C) . (p1,p2) is set
the Arrows of (C) . [p1,p2] is set
o1 is M2( the carrier of (C))
o2 is M2( the carrier of (C))
p2 is M2( the carrier of (C))
p1 is M2( the carrier of (C))
<^p2,p1^> is set
the Arrows of (C) . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of (C) . [p2,p1] is set
<^o2,o1^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of (C) . [o2,o1] is set
n is set
<^p1,p2^> is set
the Arrows of (C) . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of (C) . [p1,p2] is set
the Arrows of (C) . i is set
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
n2 is M2(<^p1,p2^>)
n2 " is M2(<^p2,p1^>)
n1 is M2(<^o1,o2^>)
the Arrows of ((C)) . (o1,o2) is set
the Arrows of ((C)) . [o1,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
((C)) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of (C)
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of ((C)) is non empty set
the carrier of (C) is non empty set
the carrier of (C) is non empty set
the carrier of C is non empty set
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
i is set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of ((C)) is Relation-like [: the carrier of ((C)), the carrier of ((C)):] -defined Function-like non empty V14([: the carrier of ((C)), the carrier of ((C)):]) set
[: the carrier of ((C)), the carrier of ((C)):] is Relation-like non empty set
the Arrows of ((C)) . i is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . i is set
o1 is M2( the carrier of (C))
o2 is M2( the carrier of (C))
n2 is M2( the carrier of ((C)))
n is M2( the carrier of ((C)))
<^n2,n^> is set
the Arrows of ((C)) . (n2,n) is set
[n2,n] is V15() set
{n2,n} is set
{n2} is set
{{n2,n},{n2}} is set
the Arrows of ((C)) . [n2,n] is set
<^o2,o1^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of (C) . [o2,o1] is set
n1 is set
<^n,n2^> is set
the Arrows of ((C)) . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of ((C)) . [n,n2] is set
p2 is M2( the carrier of C)
p1 is M2( the carrier of C)
<^p2,p1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Arrows of C . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of C . [p2,p1] is set
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^o1,o2^>)
n1 is M2(<^p1,p2^>)
the Arrows of (C) . (p1,p2) is set
the Arrows of (C) . [p1,p2] is set
o1 is M2( the carrier of (C))
o2 is M2( the carrier of (C))
p2 is M2( the carrier of (C))
p1 is M2( the carrier of (C))
<^p2,p1^> is set
the Arrows of (C) . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of (C) . [p2,p1] is set
<^o2,o1^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of (C) . [o2,o1] is set
n is set
<^p1,p2^> is set
the Arrows of (C) . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of (C) . [p1,p2] is set
the Arrows of (C) . i is set
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
n2 is M2(<^p1,p2^>)
n2 " is M2(<^p2,p1^>)
n1 is M2(<^o1,o2^>)
the Arrows of ((C)) . (o1,o2) is set
the Arrows of ((C)) . [o1,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
((C)) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of (C)
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of ((C)) is non empty set
the carrier of (C) is non empty set
the carrier of (C) is non empty set
the carrier of C is non empty set
i is set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of ((C)) is Relation-like [: the carrier of ((C)), the carrier of ((C)):] -defined Function-like non empty V14([: the carrier of ((C)), the carrier of ((C)):]) set
[: the carrier of ((C)), the carrier of ((C)):] is Relation-like non empty set
the Arrows of ((C)) . i is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . i is set
o1 is M2( the carrier of (C))
o2 is M2( the carrier of (C))
n2 is M2( the carrier of ((C)))
n is M2( the carrier of ((C)))
<^n2,n^> is set
the Arrows of ((C)) . (n2,n) is set
[n2,n] is V15() set
{n2,n} is set
{n2} is set
{{n2,n},{n2}} is set
the Arrows of ((C)) . [n2,n] is set
<^o2,o1^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of (C) . [o2,o1] is set
n1 is set
<^n,n2^> is set
the Arrows of ((C)) . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of ((C)) . [n,n2] is set
p2 is M2( the carrier of C)
p1 is M2( the carrier of C)
<^p2,p1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Arrows of C . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of C . [p2,p1] is set
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^o1,o2^>)
n1 is M2(<^p1,p2^>)
the Arrows of (C) . (p1,p2) is set
the Arrows of (C) . [p1,p2] is set
o1 is M2( the carrier of (C))
o2 is M2( the carrier of (C))
p2 is M2( the carrier of (C))
p1 is M2( the carrier of (C))
<^p2,p1^> is set
the Arrows of (C) . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of (C) . [p2,p1] is set
<^o2,o1^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of (C) . [o2,o1] is set
n is set
<^p1,p2^> is set
the Arrows of (C) . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of (C) . [p1,p2] is set
the Arrows of (C) . i is set
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
n2 is M2(<^p1,p2^>)
n2 " is M2(<^p2,p1^>)
n1 is M2(<^o1,o2^>)
the Arrows of ((C)) . (o1,o2) is set
the Arrows of ((C)) . [o1,o2] is set
C is non empty transitive V129() with_units reflexive AltCatStr
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
((C)) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of (C)
(C) is non empty transitive strict V129() with_units reflexive id-inheriting SubCatStr of C
the carrier of ((C)) is non empty set
the carrier of (C) is non empty set
the carrier of (C) is non empty set
the carrier of C is non empty set
i is set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
o1 is set
o2 is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of ((C)) is Relation-like [: the carrier of ((C)), the carrier of ((C)):] -defined Function-like non empty V14([: the carrier of ((C)), the carrier of ((C)):]) set
[: the carrier of ((C)), the carrier of ((C)):] is Relation-like non empty set
the Arrows of ((C)) . i is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . i is set
o1 is M2( the carrier of (C))
o2 is M2( the carrier of (C))
n2 is M2( the carrier of ((C)))
n is M2( the carrier of ((C)))
<^n2,n^> is set
the Arrows of ((C)) . (n2,n) is set
[n2,n] is V15() set
{n2,n} is set
{n2} is set
{{n2,n},{n2}} is set
the Arrows of ((C)) . [n2,n] is set
<^o2,o1^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of (C) . [o2,o1] is set
n1 is set
<^n,n2^> is set
the Arrows of ((C)) . (n,n2) is set
[n,n2] is V15() set
{n,n2} is set
{n} is set
{{n,n2},{n}} is set
the Arrows of ((C)) . [n,n2] is set
p2 is M2( the carrier of C)
p1 is M2( the carrier of C)
<^p2,p1^> is set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the Arrows of C . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of C . [p2,p1] is set
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
<^p1,p2^> is set
the Arrows of C . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of C . [p1,p2] is set
n2 is M2(<^o1,o2^>)
n1 is M2(<^p1,p2^>)
the Arrows of (C) . (p1,p2) is set
the Arrows of (C) . [p1,p2] is set
o1 is M2( the carrier of (C))
o2 is M2( the carrier of (C))
p2 is M2( the carrier of (C))
p1 is M2( the carrier of (C))
<^p2,p1^> is set
the Arrows of (C) . (p2,p1) is set
[p2,p1] is V15() set
{p2,p1} is set
{p2} is set
{{p2,p1},{p2}} is set
the Arrows of (C) . [p2,p1] is set
<^o2,o1^> is set
the Arrows of (C) is Relation-like [: the carrier of (C), the carrier of (C):] -defined Function-like non empty V14([: the carrier of (C), the carrier of (C):]) set
[: the carrier of (C), the carrier of (C):] is Relation-like non empty set
the Arrows of (C) . (o2,o1) is set
[o2,o1] is V15() set
{o2,o1} is set
{o2} is set
{{o2,o1},{o2}} is set
the Arrows of (C) . [o2,o1] is set
n is set
<^p1,p2^> is set
the Arrows of (C) . (p1,p2) is set
[p1,p2] is V15() set
{p1,p2} is set
{p1} is set
{{p1,p2},{p1}} is set
the Arrows of (C) . [p1,p2] is set
the Arrows of (C) . i is set
<^o1,o2^> is set
the Arrows of (C) . (o1,o2) is set
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of (C) . [o1,o2] is set
n2 is M2(<^p1,p2^>)
n2 " is M2(<^p2,p1^>)
n1 is M2(<^o1,o2^>)
the Arrows of ((C)) . (o1,o2) is set
the Arrows of ((C)) . [o1,o2] is set