Definition weq_fully_faithful_full_and_faithful (C D : precategory_data) (F : functor C D) : (fully_faithful F) ≃ (full_and_faithful F) := weqimplimpl (fully_faithful_implies_full_and_faithful _ _ F) (full_and_faithful_implies_fully_faithful _ _ F) (isaprop_fully_faithful _ _ F) (isaprop_full_and_faithful _ _ F).
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.