Definition is_universal_coproduct {B : bicat} {x p y : B} (ι₁ : x --> p) (ι₂ : y --> p) : UU := ∏ (z : B) (h : z --> p), ∑ (v w : B) (f₁ : v --> x) (f₂ : w --> y) (g₁ : v --> z) (g₂ : w --> z) (γ₁ : invertible_2cell (f₁ · ι₁) (g₁ · h)) (γ₂ : invertible_2cell (f₂ · ι₂) (g₂ · h)) (H₁ : has_pb_ump (make_pb_cone _ f₁ g₁ γ₁)) (H₂ : has_pb_ump (make_pb_cone w f₂ g₂ γ₂)), has_bincoprod_ump (make_bincoprod_cocone _ g₁ g₂).
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.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Colimits.Initial. Require Import UniMath.Bicategories.Colimits.Coproducts. Require Import UniMath.Bicategories.Limits.CommaObjects. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.PullbackFunctions. Import PullbackFunctions.Notations.