Lemma equiv_Kernel1_eq {a b : C} (f : C⟦a, b⟧) (K : Limits.Kernels.Kernel (equiv_Zero2 Z) f) : KernelArrow K · f = KernelArrow K · ZeroArrow Z a b. Proof. rewrite precomp_with_ZeroArrow. rewrite <- equiv_ZeroArrow. apply KernelCompZero. 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.Equalizers. Require Import UniMath.CategoryTheory.Limits.Kernels.