proposition: Lemma Quotcategory_isZero : isZero (C:=Quotcategory) Z.
proof: Proof. use make_isZero. - intros a. use tpair. + exact (to_quot_mor (@ZeroArrowFrom PA Z a)). + cbn beta. intros t. set (t'1 := @issurjsetquotpr (to_abgr Z a) (binopeqrel_subgr_eqrel (PAS Z a)) t). use (squash_to_prop t'1). apply has_homsets_Quotcategory. intros t1. clear t'1. induction t1 as [t1 t2]. rewrite <- t2. unfold to_quot_mor. apply maponpaths. apply ArrowsFromZero. - intros a. use tpair. + exact (to_quot_mor (@ZeroArrowTo PA Z a)). + cbn beta. intros t. set (t'1 := @issurjsetquotpr (to_abgr a Z) (binopeqrel_subgr_eqrel (PAS a Z)) t). use (squash_to_prop t'1). apply has_homsets_Quotcategory. intros t1. clear t'1. induction t1 as [t1 t2]. rewrite <- t2. unfold to_quot_mor. apply maponpaths. apply ArrowsToZero. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels