proposition: Lemma is_nat_trans_epi_from_pointwise_epis (C D : precategory) (hs : has_homsets D) (F G : ob (functor_precategory C D hs)) (α : F --> G) (H : ∏ a : ob C, isEpi (pr1 α a)) : isEpi α.
proof: Proof. intros G' β η H'. use (nat_trans_eq hs). intros x. set (H'' := nat_trans_eq_pointwise H' x). cbn in H''. apply (H x) in H''. exact H''. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Subcategory.Core UniMath.CategoryTheory.Core.Functors