Definition CokernelCoequalizer {x y : ob C} {f : x --> y} (CK : Cokernel Z f) : Coequalizer f (ZeroArrow Z _ _). Proof. use make_Coequalizer. - exact CK. - exact (CokernelArrow CK). - exact (CokernelCoequalizer_eq CK). - exact (CokernelCoequalizer_isCokernel CK). 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.