Definition weq_ff_functor_on_weq_isobandf {C D : category} {F : functor C D} (HF : fully_faithful F) (a b : C) : z_iso a b ≃ z_iso (F a) (F b). Proof. use weqbandf. - apply (make_weq _ (HF a b)). - simpl; intro f. apply weqimplimpl. + intro H. exact (pr2(functor_on_z_iso _ (_,,H))). + apply ff_reflects_is_iso. apply HF. + apply isaprop_is_z_isomorphism. + apply isaprop_is_z_isomorphism. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Univalence. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Univalence.