Lemma equiv_Kernel2_eq {a b : C} (f : C⟦a, b⟧) (K : Kernel f) : EqualizerArrow C K · f = Limits.Zero.ZeroArrow (equiv_Zero2 Z) (EqualizerObject C K) b. Proof. rewrite (EqualizerArrowEq C K). rewrite equiv_ZeroArrow. rewrite precomp_with_ZeroArrow. apply idpath. 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.