Definition global_cartesian_cleaving_comprehension : global_cartesian_disp_psfunctor cleaving_comprehension. Proof. use preserves_global_lifts_to_cartesian. - exact univalent_cat_is_univalent_2. - exact (cod_disp_univalent_2 _ univalent_cat_is_univalent_2). - exact cleaving_of_cleaving_global_cleaving. - intros C₁ C₂ F D₁. use is_pb_to_cartesian_1cell. apply reindexing_has_pb_ump. apply is_isofibration_from_is_fibration. exact (pr2 D₁). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.StreetFibration. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Reindexing. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor. Require Import UniMath.Bicategories.DisplayedBicats.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.CartesianPseudoFunctor. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DispBicatOfDispCats. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Codomain. Require Import UniMath.Bicategories.DisplayedBicats.ExamplesOfCleavings.CodomainCleaving. Require Import UniMath.Bicategories.DisplayedBicats.ExamplesOfCleavings.FibrationCleaving. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.Examples.BicatOfUnivCatsLimits. Require Import UniMath.Bicategories.Limits.Examples.OpCellBicatLimits. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.Logic.ComprehensionBicat.