(** The identity algebra homomorphism. *)
Program Definition Algebra_Hom_id (alg : Algebra) : Algebra_Hom alg alg :=
{|
Alg_map := id
|}.

(** Identity algebra homomorphism is the left unit of compositon. *)
Theorem Algebra_Hom_id_unit_left
{alg alg' : Algebra}
(f : Algebra_Hom alg alg') :
(Algebra_Hom_compose f (Algebra_Hom_id alg')) = f.