theorem
  for T being Functor of B,C for S being Functor of C,D st T is full & S
  is full holds S*T is full
proof
  let T be Functor of B,C;
  let S be Functor of C,D;
  assume that
A1: T is full and
A2: S is full;
  let b,b9 be Object of B such that
A3: Hom((S*T).b,(S*T).b9) <> {};
  let g be Morphism of (S*T).b,(S*T).b9;
A4: (S*T).b = S.(T.b) & (S*T).b9 = S.(T.b9) by Th70;
  then consider f being Morphism of T.b,T.b9 such that
A5: g = S.f by A2,A3;
A6: Hom(T.b,T.b9) <> {} by A2,A3,A4;
  hence Hom(b,b9) <> {} by A1;
  consider h being Morphism of b,b9 such that
A7: f = T.h by A1,A6;
  take h;
  thus thesis by A5,A7,FUNCT_2:15;
end;
