
theorem Th29:
  for C being Category, I being Indexing of C for T being
TargetCat of I, D being Categorial Category for F being Functor of T,D holds D
  is TargetCat of F*I
proof
  let C be Category;
  let I be Indexing of C;
  let T be TargetCat of I, D be Categorial Category;
  let F be Functor of T,D;
  Image F is TargetCat of F*I by Th28;
  then rng (F*I) is Subcategory of Image F by Th14;
  then rng (F*I) is Subcategory of D by CAT_5:4;
  hence thesis by Th14;
end;
