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 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;
