
theorem Th27:
  for C being Category, I being Indexing of C for T being
TargetCat of I, D,E being Categorial Category for F being Functor of T,D for G
  being Functor of T,E st F = G holds F*I = G*I
proof
  let C be Category;
  let I be Indexing of C;
  let T be TargetCat of I, D,E be Categorial Category;
  let F be Functor of T,D;
  let G be Functor of T,E;
  assume
A1: F = G;
  thus F*I = (F*(I-functor(C,T)))-indexing_of C by Def17
    .= (G*(I-functor(C,T)))-indexing_of C by A1,Th2
    .= G*I by Def17;
end;
