
theorem Th13:
  for C,D being empty with_identities CategoryStr holds C ~= D
  proof
    let C,D be empty with_identities CategoryStr;
    set F = the covariant Functor of C,D;
    set G = the covariant Functor of D,C;
    G (*) F = id C & F (*) G = id D;
    hence C ~= D by CAT_6:def 28;
  end;
