Lemma abgr_KernelArrowIn_map_property {A B C : abgr_category} (h : C --> A) (f : A --> B) (H : h · f = ZeroArrow abgr_Zero C B) (c : (C : abgr)) : (pr1 f (pr1 h c) = 1%multmonoid). Proof. use (pathscomp0 (toforallpaths _ _ _ (base_paths _ _ H) c)). use idpath. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Monoids. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.CategoriesWithBinOps. Require Import UniMath.CategoryTheory.PrecategoriesWithAbgrops. Require Import UniMath.CategoryTheory.PreAdditive. Require Import UniMath.CategoryTheory.Additive. Require Import UniMath.CategoryTheory.Abelian. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Kernels. Require Import UniMath.CategoryTheory.Limits.Cokernels. Require Import UniMath.CategoryTheory.Limits.BinDirectSums. @ZeroArrowFrom abgr_category abgr_Zero A = abgrfunfromunit A.