Definition monoid_equiv_weq_z_iso (X Y : ob monoid_precategory) : (monoidiso X Y) ≃ (z_iso X Y). Proof. use make_weq. - exact (monoid_equiv_z_iso X Y). - exact (monoid_equiv_z_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.Free_Monoids_and_Groups. Require Import UniMath.Combinatorics.Lists. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Adjunctions.Core.