Definition QuotcategoryCompMor {A B C : ob PA} {f : Quotcategory_ob_mor⟦A, B⟧} {g : Quotcategory_ob_mor⟦B, C⟧} (QPC : QuotcategoryComp f g) : Quotcategory_ob_mor⟦A, C⟧ := pr1 QPC.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.CategoriesWithBinOps. Require Import UniMath.CategoryTheory.PrecategoriesWithAbgrops. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.Kernels. Require Import UniMath.CategoryTheory.Limits.Cokernels. rewrite <- (id_left (ZeroArrowFrom y)). set (Y := to_postmor_unel A Z (@ZeroArrowFrom A Z y)). + exact (to_quot_mor (@ZeroArrowFrom PA Z a)). apply ArrowsFromZero.