Definition is_z_iso_in_subcategory_of_monics_weq (a b : subcategory_of_monics) (f : a --> b) : (is_z_isomorphism (pr1 f)) ≃ (is_z_isomorphism f). Proof. use weqimplimpl. + use is_z_iso_in_subcategory_of_monics_from_is_z_iso. + use is_z_iso_from_is_z_iso_in_subcategory. + use (isaprop_is_z_isomorphism). + use (isaprop_is_z_isomorphism). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.covyoneda. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Subcategory.Core.