
theorem Th13:
  for C1,C2 being with_identities CategoryStr,
      f1,f2 being morphism of C1, F being Functor of C1,C2
  st F is covariant & f1 |> f2
  holds F.f1 |> F.f2 & F.(f1(*)f2) = (F.f1) (*) (F.f2)
  proof
    let C1,C2 be with_identities CategoryStr;
    let f1,f2 be morphism of C1;
    let F be Functor of C1,C2;
    assume F is covariant;
    then
A1: F is multiplicative by CAT_6:def 25;
    assume f1 |> f2;
    hence thesis by A1,CAT_6:def 23;
  end;
