Lemma commring_iso_equiv (X Y : ob commring_category) : z_iso X Y -> ringiso (X : commring) (Y : commring). Proof. intro f. use make_ringiso. - exact (make_weq (pr1 (pr1 f)) (commring_iso_is_equiv X Y f)). - exact (pr2 (pr1 f)). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence.