Definition intersection_disp_map_bicat {B : bicat} (D₁ D₂ : disp_map_bicat B) : disp_map_bicat B. Proof. use make_disp_map_bicat. - exact (intersection_arrow_subbicat D₁ D₂). - intros ? ? ? ? ? ? ? ? ? Hf pb_sqr. split ; split. + exact (pb_preserves_pred_ob D₁ (pr1 Hf) pb_sqr). + exact (pb_preserves_pred_ob D₂ (pr2 Hf) pb_sqr). + exact (mor_of_pb_preserves_pred_ob D₁ (pr1 Hf) pb_sqr). + exact (mor_of_pb_preserves_pred_ob D₂ (pr2 Hf) pb_sqr). - intros x y z f g H. exact (pr122 D₁ _ _ _ _ _ (pr1 H)). - intros ? ? ? ? ? ? ? ? ? pb_sqr ? ? ? ? ? ? ? Hf Hp₁ Hcp₁. split. + exact (pred_mor_closed_under_pb_ump_mor D₁ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (pr1 Hf) (pr1 Hp₁) (pr1 Hcp₁)). + exact (pred_mor_closed_under_pb_ump_mor D₂ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (pr2 Hf) (pr2 Hp₁) (pr2 Hcp₁)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Morphisms.Properties.ContainsAdjEquiv. Require Import UniMath.Bicategories.Morphisms.Properties.Composition. Require Import UniMath.Bicategories.Morphisms.Properties.ClosedUnderPullback. Require Import UniMath.Bicategories.Morphisms.Properties.FromInitial. Require Import UniMath.Bicategories.Colimits.Initial. Require Import UniMath.Bicategories.Limits.Pullbacks.