proposition: 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: Proof. apply (Pushouts_pw_epi (D:=hset_category)). apply PushoutsHSET_from_Colims. apply h. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Epis UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.EpiFacts UniMath.CategoryTheory.Limits.Coequalizers