Section Category_comp.
Variable C : category.
Definition comp_hom (a b c : C) (g : Hom b c) (f : Hom a b) :=
Hom_comp a b c (couple g f).
intros a b c x x' y y' H' H'0; try assumption.
unfold comp_hom in |- *; auto with algebra.
Qed.
exact (Hom_comp_assoc_prf (c:=C)).
Qed.
exact (Hom_comp_unit_l_prf (c:=C)).
Qed.

Lemma comp_hom_unit_r :
forall (a b : C) (f : Hom a b), Equal (comp_hom f (Hom_id a)) f.