Definition reindex_of_disp_functor_data : disp_functor_data (functor_identity _) (reindex_disp_cat F D₁) (reindex_disp_cat F D₂). Proof. simple refine (_ ,, _). - exact (λ x xx, G (F x) xx). - exact (λ x y xx yy f ff, ♯ G ff). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. 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.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Section IsCartesianFromReindexDispCat. End IsCartesianFromReindexDispCat. Section IsOpCartesianFromReindexDispCat. End IsOpCartesianFromReindexDispCat.