
theorem Th29:
  for C,C1,C2 being category, F1 being Functor of C,C1,
  F2 being Functor of C,C2 st F1 is covariant & F2 is covariant
  holds (C1 ->OrdC1)(*)F1 = (C2 ->OrdC1)(*)F2
  proof
    let C,C1,C2 be category;
    let F1 be Functor of C,C1;
    let F2 be Functor of C,C2;
    assume
A1: F1 is covariant & F2 is covariant;
    consider F be Functor of C, OrdC 1 such that
A2: F is covariant & for F1 being Functor of C, OrdC 1
    st F1 is covariant holds F = F1 by Def4;
    reconsider F11 = (C1 ->OrdC1)(*)F1 as covariant Functor of C, OrdC 1
    by A1,CAT_6:35;
    reconsider F22 = (C2 ->OrdC1)(*)F2 as covariant Functor of C, OrdC 1
    by A1,CAT_6:35;
    F11 = F & F22 = F by A2;
    hence thesis;
  end;
