Lemma equiv_Cokernel1_eq {a b : C} (f : C⟦a, b⟧) (CK : Limits.Cokernels.Cokernel (equiv_Zero2 Z) f) : f · (CokernelArrow CK) = ZeroArrow Z a b · (CokernelArrow CK). Proof. rewrite CokernelCompZero. rewrite postcomp_with_ZeroArrow. apply equiv_ZeroArrow. 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.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Zero. Require Import UniMath.CategoryTheory.Limits.Graphs.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Cokernels.