Lemma is_iso_isEpi {x y : C} (f : x --> y) (H : is_z_isomorphism f) : isEpi f. Proof. apply make_isEpi. intros z g h X. apply (pre_comp_with_z_iso_is_inj H). exact X. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Core.Functors.