Lemma fully_faithful_inv_hom_is_inv {C D : precategory} {F : functor C D} (FF : fully_faithful F) {a b : ob C} (f : C⟦a, b⟧) : FF^-1 (# F f) = f. Proof. cbn. apply invmap_eq. reflexivity. 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.