Definition disp_functor_data {C' C : precategory_data} (F : functor_data C' C) (D' : disp_cat_data C') (D : disp_cat_data C) := ∑ (Fob : ∏ x, D' x -> D (F x)), ∏ x y (xx : D' x) (yy : D' y) (f : x --> y), (xx -->[f] yy) -> (Fob _ xx -->[ # F f ] Fob _ yy).
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.