Lemma isCokernel_paths {x y z : C} (f : x --> y) (g : y --> z) (H H' : f · g = (ZeroArrow Z x z)) (isC : isCokernel f g H) : isCokernel f g H'. Proof. assert (e : H = H') by apply hs. induction e. exact isC. 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.