Lemma CokernelOfZeroArrow_isCokernel (x y : C) : isCokernel (ZeroArrow Z x y) (identity y) (id_right (ZeroArrow Z x y)). Proof. use make_isCokernel. intros w h H'. use unique_exists. - exact h. - exact (id_left _). - intros y0. apply hs. - intros y0 t. cbn in t. rewrite id_left in t. exact t. 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.