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;
