Definition Coequalizer {x y : A} (f1 f2 : y --> x) : Coequalizer f1 f2 := make_Coequalizer f1 f2 (PushoutIn1 (Coequalizer_Pushout f1 f2)) (Coequalizer_eq2 f1 f2) (isCoequalizer f1 f2).
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Algebra.Monoids. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Kernels. Require Import UniMath.CategoryTheory.Limits.Cokernels. Require Import UniMath.CategoryTheory.Limits.Pushouts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Opp. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.CategoriesWithBinOps. Require Import UniMath.CategoryTheory.PrecategoriesWithAbgrops. Require Import UniMath.CategoryTheory.PreAdditive. isKernel (to_Zero A) (ZeroArrowFrom x) M (ArrowsFromZero A (to_Zero A) y (ZeroArrowFrom x · M) (ZeroArrow (to_Zero A) _ _)). make_Kernel (to_Zero A) (ZeroArrowFrom _) M _ (MonicKernelZero_isKernel M). - intros y0 Y. apply ArrowsFromZero.