Definition weq_ff_functor_on_z_iso {C D : category}{F : functor C D} (HF : fully_faithful F) (a b : ob C) : z_iso a b ≃ z_iso (F a) (F b). Proof. exists (functor_on_z_iso F). apply (isweq_iso _ (iso_from_fully_faithful_reflection HF (a:=a)(b:=b))). - apply iso_from_fully_faithful_reflection_functor_on_iso. - apply functor_on_iso_iso_from_fully_faithful_reflection. 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.