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 Th29:
  C is non empty & D is empty implies not ex F being Functor of C,D st
  F is multiplicative or F is antimultiplicative
  proof
    assume
A1: C is non empty;
    then reconsider f = the Object of C as morphism of C by TARSKI:def 3;
A2: f |> f by A1,Th23;
    assume
A3: D is empty;
    assume ex F being Functor of C,D st F is multiplicative
    or F is antimultiplicative;
    then consider F be Functor of C,D such that
A4: F is multiplicative or F is antimultiplicative;
A5: not F.f |> F.f by A3;
    per cases by A4;
    suppose F is multiplicative;
      hence thesis by A5,A2;
    end;
    suppose F is antimultiplicative;
      hence thesis by A5,A2;
    end;
  end;
