Definition disp_has_binprod_univ_cat_with_pb : disp_has_binprod disp_bicat_pullback has_binprod_bicat_of_univ_cats. Proof. use subbicat_disp_binprod. - intros C₁ C₂. apply pullbacks_in_product_category. + exact (pr12 C₁). + exact (pr12 C₂). - intros C₁ C₂. apply pr1_preserves_pullback. + exact (pr12 C₁). + exact (pr12 C₂). - intros C₁ C₂. apply pr2_preserves_pullback. + exact (pr12 C₁). + exact (pr12 C₂). - intros C₁ C₂ q. apply preserves_pullback_bindelta_pair_functor. + exact (pr22 (binprod_cone_pr1 q)). + exact (pr22 (binprod_cone_pr2 q)). 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.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Categories.EilenbergMoore. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.IsoCommaCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.Limits.Examples.UnitCategoryLimits. Require Import UniMath.CategoryTheory.Limits.Examples.CategoryProductLimits. Require Import UniMath.CategoryTheory.Limits.Examples.IsoCommaLimits. Require Import UniMath.CategoryTheory.Limits.Examples.EilenbergMooreLimits. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Examples.StructuredCategories. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sub1Cell. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Prod. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax. Require Import UniMath.Bicategories.Limits.Final. Require Import UniMath.Bicategories.Limits.Products. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.EilenbergMooreObjects. Require Import UniMath.Bicategories.Limits.Examples.BicatOfUnivCatsLimits. Require Import UniMath.Bicategories.Limits.Examples.TotalBicategoryLimits. Require Import UniMath.Bicategories.Limits.Examples.DispConstructionsLimits. Require Import UniMath.Bicategories.Limits.Examples.SubbicatLimits. Require Import UniMath.Bicategories.Monads.Examples.MonadsInTotalBicat. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Examples.MonadInclusion.