Definition cat_with_pullback_has_RezkCompletion : disp_left_universal_arrow LUR (disp_psfunctor_on_cat_to_univ_cat disp_bicat_have_pullbacks (disp_2cells_isaprop_from_disp_2cells_iscontr _ disp_2cells_is_contr_have_pullbacks)).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.WeakEquivalences.Core. Require Import UniMath.CategoryTheory.WeakEquivalences.Preservation.Pullbacks. Require Import UniMath.CategoryTheory.WeakEquivalences.Reflection.Pullbacks. Require Import UniMath.CategoryTheory.WeakEquivalences.Creation.Pullbacks. Require Import UniMath.CategoryTheory.WeakEquivalences.LiftPreservation.Pullbacks. 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.Core.Examples.BicatOfCats. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.PseudoFunctors.UniversalArrow. Import PseudoFunctor.Notations. Import DispBicat.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Examples.BicatOfCatToUnivCat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DispBicatOnCatToUniv. Require Import UniMath.Bicategories.DisplayedBicats.Examples.CategoriesWithStructure. Require Import UniMath.Bicategories.DisplayedBicats.DisplayedUniversalArrow. Require Import UniMath.Bicategories.DisplayedBicats.DisplayedUniversalArrowOnCat.