Definition KernelCompMonic_mor1 {x y z : C} (f : x --> y) (M : Monic C y z) (K1 : Kernel Z (f · M)) (K2 : Kernel Z f) : C⟦K1, K2⟧ := KernelIn Z K2 _ (KernelArrow K1) (KernelCompMonic_eq1 f M K1 K2).
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.