Lemma pregroupoid_hom_weq_iso {pgpd : pregroupoid} (a b : pgpd) : (a --> b) ≃ z_iso a b. Proof. use weq_iso. - intros f; refine (f,, _); apply pregroupoid_is_pregroupoid. - apply pr1. - reflexivity. - intro; apply z_iso_eq; reflexivity. Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.opp_precat.