reserve A,B,C for Category,
  F,F1,F2,F3 for Functor of A,B,
  G for Functor of B, C;
reserve m,o for set;
reserve t for natural_transformation of F,F1,
  t1 for natural_transformation of F1,F2;

theorem
  id F is natural_equivalence of F,F
proof
  thus F ~= F;
  let a be Object of A;
  (id F).a = id(F.a) by Th16;
  hence thesis by CAT_1:44;
end;
