Definition CoequalizerCokernel {x y : ob C} {f : x --> y} (CE : Coequalizer f (ZeroArrow Z _ _)) : Cokernel Z f. Proof. use make_Cokernel. - exact CE. - exact (CoequalizerArrow CE). - exact (CoequalizerCokernel_eq CE). - exact (CoequalizerCokernel_isCokernel CE). Defined.
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.