
theorem Th11:
  for C,D being category, F being Functor of C,D st
  F is covariant holds F (*) id C = F & id D (*) F = F
  proof
    let C,D be category;
    let F be Functor of C,D;
    assume
A1: F is covariant;
    thus F (*) id C = (id C) * F by A1,CAT_6:def 27
    .= (id the carrier of C) * F by STRUCT_0:def 4
    .= F by FUNCT_2:17;
    thus id D (*) F = F * (id D) by A1,CAT_6:def 27
    .= F * (id the carrier of D) by STRUCT_0:def 4
    .= F by FUNCT_2:17;
  end;
