Definition commrig_equiv_weq_iso (X Y : ob commrig_category) : (rigiso (X : commrig) (Y : commrig)) ≃ (z_iso X Y). Proof. use make_weq. - exact (commrig_equiv_iso X Y). - exact (commrig_equiv_iso_is_equiv X Y). 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.