reserve C for CatStr;
reserve f,g for Morphism of C;
reserve C for non void non empty CatStr,
  f,g for Morphism of C,
  a,b,c,d for Object of C;
reserve o,m for set;
reserve B,C,D for Category;
reserve a,b,c,d for Object of C;
reserve f,f1,f2,g,g1,g2 for Morphism of C;
reserve f,f1,f2 for Morphism of a,b;
reserve f9 for Morphism of b,a;
reserve g for Morphism of b,c;
reserve h,h1,h2 for Morphism of c,d;

theorem
  for T being Functor of B,C for S being Functor of C,D st T is faithful
  & S is faithful holds S*T is faithful
proof
  let T be Functor of B,C;
  let S be Functor of C,D;
  assume that
A1: T is faithful and
A2: S is faithful;
  let b,b9 be Object of B such that
A3: Hom(b,b9) <> {};
  let f1,f2 be Morphism of b,b9;
A4: T.f2 is Morphism of T.b,T.b9 by A3,Th78;
  assume
A5: (S*T).f1 = (S*T).f2;
A6: (S*T).f1 = S.(T.f1) & (S*T).f2 = S.(T.f2) by FUNCT_2:15;
  Hom(T.b,T.b9) <> {} & T.f1 is Morphism of T.b,T.b9 by A3,Th78,Th79;
  then T.f1 = T.f2 by A2,A5,A6,A4;
  hence thesis by A1,A3;
end;
