reserve B,C,D,C9,D9 for Category;
reserve E for Subcategory of C;

theorem
  for T being Functor of C,D, T9 being Functor of C,D9, c being Object
  of C holds (Obj <:T,T9:>).c = [(Obj T).c,(Obj T9).c]
proof
  let T be Functor of C,D, T9 be Functor of C,D9, c be Object of C;
A1: T.(id c) = id((Obj T).c) & T9.(id c) = id((Obj T9).c) by CAT_1:68;
  <:T,T9:>.(id c) = [T.(id c),T9.(id c)] & [id((Obj T).c),id((Obj T9).c)]
  = id [(Obj T).c,(Obj T9).c] by Th25,FUNCT_3:59;
  hence thesis by A1,CAT_1:67;
end;
