theorem Th69:
  id the carrier' of C is Functor of C,C
proof
  set F = id the carrier of C;
  set T = id the carrier' of C;
   (for c being Object of C holds T.(id c) = id(F.c)) &
   (for f being Morphism of C holds F.(dom f) = dom (T.f) & F.(cod f) =
    cod (T.f)) &
    for f,g being Morphism of C st  dom g = cod f
     holds T.(g(*)f) = (T.g)(*)(T.f);
  hence thesis by Th60;
end;
