Definition CokernelOfIdentity (x : C) : Cokernel (identity x). Proof. use make_Cokernel. - exact Z. - exact (ZeroArrowTo x). - use ArrowsToZero. - exact (CokernelOfIdentity_isCokernel x). 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.Epis. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Zero. - exact (ZeroArrowFrom w). - intros y X. cbn in X. use ArrowsFromZero.