reserve C for CategoryStr;
reserve f,f1,f2,f3 for morphism of C;
reserve g1,g2 for morphism of C opp;
reserve C,D,E for with_identities CategoryStr;
reserve F for Functor of C,D;
reserve G for Functor of D,E;
reserve f for morphism of C;

theorem
  for C,D being non empty composable with_identities CategoryStr,
      F being covariant Functor of C,D,
      o being Object of C holds F.(id- o) = id-(F.o) by Def21;
