
theorem Th24:
  for C,D being Category, F being Functor of C,D, I being Indexing
  of D for T being TargetCat of I holds T is TargetCat of I*F
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;
  set T9 = the TargetCat of I*F;
  rng (I*F) = Image ((I*F)-functor(C,T9)) & I*F = ((I-functor(D,T))*F)
  -indexing_of C by Def12,Th23;
  then rng (I*F) = Image ((I-functor(D,T))*F) by Th18,CAT_5:22;
  hence thesis by Th14;
end;
