Definition CokernelCommutes {y z : C} {g : y --> z} (CK : Cokernel g) (w : C) (h : z --> w) (H : g · h = ZeroArrow Z y w) : (CokernelArrow CK) · (CokernelOut CK w h H) = h := pr2 (iscontrpr1 (CokernelisCokernel CK w h H)).
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.