Lemma fiber_functor_ff {C C' : category} {D} {D'} {F : functor C C'} (FF : disp_functor F D D') (H : disp_functor_ff FF) (c : C) : fully_faithful (fiber_functor FF c). Proof. intros xx yy; cbn. set (XR := H _ _ xx yy (identity _ )). apply twooutof3c. - apply XR. - apply isweqtransportf. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Total.