Definition disp_nat_trans_axioms {C' C : precategory_data} {F' F : functor_data C' C} {a : nat_trans F' F} {D' : disp_cat_data C'} {D : disp_cat_data C} {R' : disp_functor_data F' D' D} {R : disp_functor_data F D' D} (b : disp_nat_trans_data a R' R) : UU := forall (x' x : C') (f : x' --> x) (xx' : D' x') (xx : D' x) (ff : xx' -->[ f ] xx), ♯ R' ff ;; b _ xx = transportb _ (nat_trans_ax a _ _ f ) (b _ xx' ;; ♯ R 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.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.