Program Definition Comma_Hom_id (a : Comma_Obj) : Comma_Hom a a :=
    {|
      CMH_left := id;
      CMH_right := id
    |}.

(* Specifications: *)
Theorem Comma_Hom_id_unit_left {a b : Comma_Obj} (h : Comma_Hom a b) : Comma_Hom_compose h (Comma_Hom_id b) = h.
Theorem Comma_Hom_id_unit_right {a b : Comma_Obj} (h : Comma_Hom a b) : Comma_Hom_compose (Comma_Hom_id a) h = h.