Library CT.Instance.Algebra.Rng
Program Definition RngCategory (T : Type) : Category :=
{| ob := @Rng T;
mor := RngHomomorphism;
comp := fun _ _ _ ⇒ rng_hom_composition;
id := fun _ ⇒ rng_hom_id;
assoc := fun _ _ _ _ ⇒ rng_hom_composition_assoc
|}.
Next Obligation.
Proof.
symmetry.
apply rng_hom_composition_assoc.
Qed.
Next Obligation.
Proof. apply rng_hom_eq. reflexivity. Qed.
Next Obligation.
Proof. apply rng_hom_eq. reflexivity. Qed.
{| ob := @Rng T;
mor := RngHomomorphism;
comp := fun _ _ _ ⇒ rng_hom_composition;
id := fun _ ⇒ rng_hom_id;
assoc := fun _ _ _ _ ⇒ rng_hom_composition_assoc
|}.
Next Obligation.
Proof.
symmetry.
apply rng_hom_composition_assoc.
Qed.
Next Obligation.
Proof. apply rng_hom_eq. reflexivity. Qed.
Next Obligation.
Proof. apply rng_hom_eq. reflexivity. Qed.