Lemma KernelInPaths_is_iso {x y : C} {f f' : x --> y} (e : f = f') (K1 : Kernel Z f) (K2 : Kernel Z f') : is_iso (KernelInPaths_is_iso_mor e K1 K2). Proof. induction e. apply KernelsIn_is_iso. 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.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.