
theorem Th23:
  for C,D being Category, F being Functor of C,D, I being Indexing
of D for T being TargetCat of I holds I*F = ((I-functor(D,T))*F)-indexing_of C
proof
  let C,D be Category;
  let F be Functor of C,D;
  let I be Indexing of D;
  let T be TargetCat of I;
  Image F is Subcategory of D;
  then
A1: I*F = (I-functor(D,rng I)*F)-indexing_of C by Def16;
  (I-functor(D,rng I))*F = (I-functor(D,T))*F by Th11;
  hence thesis by A1,Th2;
end;
