Lemma abmonoid_equiv_z_iso (X Y : ob abmonoid_category) : monoidiso (X : abmonoid) (Y : abmonoid) -> z_iso X Y. Proof. intros f. exists (monoidfunconstr (pr2 f)). exact (abmonoid_equiv_is_z_iso X Y 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.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence.