proposition: 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: Proof. intros xx yy; cbn. set (XR := H _ _ xx yy (identity _ )). apply twooutof3c. - apply XR. - apply isweqtransportf. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Total