Definition KernelCompMonic {x y z : C} (f : x --> y) (M : Monic C y z) (K : Kernel Z (f · M)) : Kernel Z f. Proof. use make_Kernel. - exact K. - use KernelArrow. - exact (KernelCompMonic_eq f M K). - exact (KernelCompMonic_isKernel f M K). 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.