reserve A,B,C for Category,
  F,F1 for Functor of A,B;
reserve o,m for set;
reserve t for natural_transformation of F,F1;

theorem Th33:
  for F being Functor of A,B, G being Functor of A,C for a being
  Object of A holds <:F,G:>.a = [F.a,G.a]
proof
  let F be Functor of A,B, G be Functor of A,C;
  let a be Object of A;
  <:F,G:>.(id a qua Morphism of A) = [F.(id a qua Morphism of A),G.(id a
  qua Morphism of A)] by FUNCT_3:59
    .= [id(F.a),G.(id a qua Morphism of A)] by CAT_1:71
    .= [id(F.a),id(G.a)] by CAT_1:71
    .= id[F.a,G.a] by CAT_2:31;
  hence thesis by CAT_1:70;
end;
