Lemma CoequalizerCokernel_eq {x y : ob C} {f : x --> y} (CE : Coequalizer f (ZeroArrow Z _ _)) : f · CoequalizerArrow CE = ZeroArrow Z x CE. Proof. rewrite <- (ZeroArrow_comp_left _ _ _ _ _ (CoequalizerArrow CE)). exact (CoequalizerEqAr CE). 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.