Lemma EffectiveEpis_Functor_HSET : EpisAreEffective C_SET. Proof. intros F G m isepim. apply (isEffectivePw (D:=hset_category)). intro x. apply EffectiveEpis_HSET. apply (Pushouts_pw_epi (D:=hset_category) PushoutsHSET_from_Colims). assumption. 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.