Definition univalent_reindex_cat {C₁ C₂ : univalent_category} (F : C₁ ⟶ C₂) (D : disp_univalent_category C₂) : univalent_category. Proof. use make_univalent_category. - exact (total_category (reindex_disp_cat F (pr1 D))). - use is_univalent_total_category. + exact (pr2 C₁). + exact (is_univalent_reindex_disp_cat F _ (pr2 D)). 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.