reserve C for CategoryStr;
reserve f,f1,f2,f3 for morphism of C;
reserve g1,g2 for morphism of C opp;

theorem Th10:
  C is empty implies f is identity
  proof
    assume C is empty;
    then (for f1 being morphism of C st f |> f1 holds f (*) f1 = f1) &
    (for f1 being morphism of C st f1 |> f holds f1 (*) f = f1);
    then f is left_identity & f is right_identity;
    hence f is identity;
  end;
