Lemma pregroupoid_hom_weq_iso_comp {pgpd : pregroupoid} {a b c : ob pgpd} (f : a --> b) (g : b --> c) : z_iso_comp (pregroupoid_hom_weq_iso _ _ f) (pregroupoid_hom_weq_iso _ _ g) = (pregroupoid_hom_weq_iso _ _ (f · g)). Proof. 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.