Lemma isEpi_pw_pr_quot_functor : ∏ x, isEpi (pr_quot_functor x). Proof. intros a z f g eqfg. apply funextfun. intro x. eapply surjectionisepitosets. apply issurjsetquotpr. apply setproperty. intro u. apply toforallpaths in eqfg. apply eqfg. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.MonoEpiIso. Require Import UniMath.CategoryTheory.Categories.HSET.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Structures. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.EpiFacts. Require Import UniMath.CategoryTheory.Limits.Coequalizers.