Definition closed_under_pb_ump_mor : UU := ∏ (pb x y z : B) (f : x --> z) (g : y --> z) (p₁ : pb --> x) (p₂ : pb --> y) (γ : invertible_2cell (p₁ · f) (p₂ · g)) (H : has_pb_ump (make_pb_cone pb p₁ p₂ γ)) (cc c : B) (cp₁ : cc --> x) (cp₂ : cc --> c) (h : c --> y) (δ : invertible_2cell (cp₁ · f) ((cp₂ · h) · g)) (cone := make_pb_cone cc cp₁ (cp₂ · h) δ), pred_ob D f → pred_mor D p₂ f p₁ → pred_mor D cp₂ f cp₁ → pred_mor D cp₂ p₂ (pb_ump_mor H cone).
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.