Lemma disp_functor_transportf {C' C : category} {D' : disp_cat C'} {D : disp_cat C} (F : functor C' C) (FF : disp_functor F D' D) (x' x : C') (f' f : x' --> x) (p : f' = f) (xx' : D' x') (xx : D' x) (ff : xx' -->[ f' ] xx) : ♯ FF (transportf _ p ff) = transportf _ (maponpaths (# F) p) (♯FF ff). Proof. induction p. apply idpath. Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.