Definition make_disp_map_bicat_with_pb (B : bicat_with_pb) (D : arrow_subbicat B) (closed_pb : closed_under_pb D) (closed_pb_mor : closed_under_pb_ump_mor D) : disp_map_bicat B. Proof. refine (make_disp_map_bicat D closed_pb _ closed_pb_mor). intros x y z f g p. pose (cone := pr1 (pr2 B x y z f g)). pose (pb_ump := pr2 (pr2 B x y z f g)). simple refine (_ ,, _ ,, _ ,, _ ,, _). - exact cone. - exact (pb_cone_pr1 cone). - exact (pb_cone_pr2 cone). - exact (pb_cone_cell cone). - exact pb_ump. 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.