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

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