Lemma KernelArrowisMonic {y z : C} {g : y --> z} (K : Kernel g) : isMonic (KernelArrow K). Proof. apply make_isMonic. intros z0 g0 h X. use KernelInsEq. exact X. 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.Monics. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Zero. isKernel (ZeroArrowFrom x) (identity x) (ArrowsFromZero C Z x (ZeroArrowFrom x · identity x) (ZeroArrow Z Z x)). - exact (ZeroArrowFrom x). - use ArrowsFromZero.