
theorem
  for C1,C2 being category st C1 ~= C2 holds C1 is empty iff C2 is empty
  proof
    let C1,C2 be category;
    assume C1 ~= C2;
    then consider F be Functor of C1,C2, G be Functor of C2,C1 such that
A1: F is covariant & G is covariant & G (*) F = id C1 & F (*) G = id C2
    by CAT_6:def 28;
    thus thesis by A1,CAT_6:31;
  end;
