Definition CokernelEpiComp {x y z : C} (E : Epi C x y) (f : y --> z) (CK : Cokernel Z (E · f)) : Cokernel Z f. Proof. use make_Cokernel. - exact CK. - use CokernelArrow. - exact (CokernelEpiComp_eq E f CK). - exact (CokernelEpiComp_isCoequalizer E f CK). 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.