
theorem Th21:
  for C1,C2 being Category, F being Functor of C1,C2 for a,b being
  Object of C1 holds (Upsilon F).homsym(a,b) = homsym(F.a,F.b)
proof
  let C1,C2 be Category, F be Functor of C1,C2;
  let a,b be Object of C1;
A1: dom Obj F = the carrier of C1 by FUNCT_2:def 1;
  thus (Upsilon F).homsym(a,b) = [0,(Obj F)*(homsym(a,b))`2] by Def11
    .= [0,(Obj F)*<*a,b*>]
    .= [0,<*(Obj F).a,(Obj F).b*>] by A1,FINSEQ_2:125
    .= [0,<*F.a,(Obj F).b*>]
    .= homsym(F.a,F.b);
end;
