reserve A,B,C for Category,
  F,F1,F2,F3 for Functor of A,B,
  G for Functor of B, C;
reserve m,o for set;

theorem Th11:
  for a being Object of A holds F/.id a = id (F.a)
proof
  let a be Object of A;
  Hom(a,a) <> {};
  hence F/.id a = F.((id a) qua Morphism of A) by CAT_3:def 10
    .= id (F.a) by CAT_1:71;
end;
