Definition iso_from_fully_faithful_reflection {C D : precategory} {F : functor C D} (HF : fully_faithful F) {a b : ob C} (f : z_iso (F a) (F b)) : z_iso a b. Proof. exists (fully_faithful_inv_hom HF a b f). apply fully_faithful_reflects_iso_proof. 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.