proposition: Lemma monic_epi_is_iso {x y : A} {f : x --> y} : isMonic f -> isEpi f -> is_z_isomorphism f.
proof: Proof. intros iM iE. use make_is_z_isomorphism. - exact (KernelIn (to_Zero A) (MonicToKernel (make_Monic _ _ iM)) y (identity y) (monic_epi_is_iso_eq iM iE)). - exact (monic_epi_is_iso_inverses iM iE). Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Algebra.Monoids UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Opp UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive