Lemma abmonoid_iso_equiv_is_equiv (X Y : ob abmonoid_category) : isweq (abmonoid_iso_equiv X Y). Proof. use isweq_iso. - exact (abmonoid_equiv_z_iso X Y). - intros x. use z_iso_eq. use monoidfun_paths. use idpath. - intros y. use monoidiso_paths. use subtypePath. + intros x0. use isapropisweq. + use idpath. 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.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence.