Definition disp_has_pb (HB : has_pb B) : UU := ∏ (x y z : total_bicat D) (f : x --> z) (g : y --> z), let p_cone : pb_cone (pr1 f) (pr1 g) := pr1 (HB _ _ _ (pr1 f) (pr1 g)) in let Hp_cone : has_pb_ump p_cone := pr2 (HB _ _ _ (pr1 f) (pr1 g)) in ∑ (pb : D (pb_cone_obj p_cone)), pb -->[ pb_cone_pr1 p_cone ] pr2 x × pb -->[ pb_cone_pr2 p_cone ] pr2 y × ∏ (q : pb_cone f g), pr21 q -->[ pb_ump_mor Hp_cone (total_pb_cone_help_cone q) ] pb.
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.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EndoMap. 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.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.