Lemma is_pointwise_epi_from_set_nat_trans_epi (C:category) (F G : functor C hset_precategory) (f:nat_trans F G) (h:isEpi (C:=functor_category C HSET) f) : ∏ (x:C), isEpi (f x). Proof. apply (Pushouts_pw_epi (D:=hset_category)). apply PushoutsHSET_from_Colims. apply h. 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.