Definition disp_functor_on_objects {C' C : precategory_data} {F : functor_data C' C} {D' : disp_cat_data C'} {D : disp_cat_data C} (FF : disp_functor_data F D' D) {x : C'} (xx : D' x) : D (F x) := pr1 FF x xx.
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.