Definition is_disjoint_coproduct {B : bicat_with_biinitial} {x p y : B} (ι₁ : x --> p) (ι₂ : y --> p) : UU := fully_faithful_1cell ι₁ × fully_faithful_1cell ι₂ × has_comma_ump (biinitial_comma_cone ι₁ ι₂) × has_comma_ump (biinitial_comma_cone ι₂ ι₁).
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.