Definition disp_functor_axioms {C' C : category} {F : functor C' C} {D' : disp_cat C'} {D : disp_cat C} (FF : disp_functor_data F D' D) := (∏ x (xx : D' x), ♯ FF (id_disp xx) = transportb _ (functor_id F x) (id_disp (FF _ xx))) × (∏ x y z (xx : D' x) yy zz (f : x --> y) (g : y --> z) (ff : xx -->[f] yy) (gg : yy -->[g] zz), ♯ FF (ff ;; gg) = transportb _ (functor_comp F f g) (♯ FF ff ;; ♯ FF gg)).
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.