Definition Kernel_up_to_iso {x y z : C} (f : x --> y) (g : y --> z) (K : Kernel Z g) (h : z_iso x K) (H : f = h · (KernelArrow K)) : Kernel Z g := make_Kernel Z f _ (Kernel_up_to_iso_eq f g K h H) (Kernel_up_to_iso_isKernel f g K h H (Kernel_up_to_iso_eq f g K h H)).
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.