theorem Th78:
  for T being Functor of C,D for c,c9 being Object of C st Hom(c,
  c9) <> {} for f being Morphism of c,c9 holds T.f is Morphism of T.c,T.c9
proof
  let T be Functor of C,D;
  let c,c9 be Object of C such that
A1: Hom(c,c9) <> {};
  let f be Morphism of c,c9;
  T.f in Hom(T.c,T.c9) by A1,Th77;
  hence thesis by Def3;
end;
