Lemma CokernelCoequalizer_eq {x y : ob C} {f : x --> y} (CK : Cokernel Z f) : f · CokernelArrow CK = ZeroArrow Z x y · CokernelArrow CK. Proof. rewrite ZeroArrow_comp_left. use CokernelCompZero. 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.Epis. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Zero. - exact (ZeroArrowFrom w). - intros y X. cbn in X. use ArrowsFromZero.