Definition disp_functor_on_morphisms {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 y : C'} {xx : D' x} {yy} {f : x --> y} (ff : xx -->[f] yy) : (FF _ xx) -->[ # F f ] (FF _ yy) := pr2 FF x y xx yy f ff.
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.