Definition Kernel_up_to_iso2 {x y z : C} {f1 : x --> y} {f2 : x --> z} {h : z_iso y z} (H : f1 · h = f2) (K : Kernel Z f1) : Kernel Z f2 := make_Kernel Z (KernelArrow K) _ (Kernel_up_to_iso2_eq h H K) (Kernel_up_to_iso2_isKernel f1 f2 h H K).
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.