Definition has_bincoprod_slice_bicat {B : bicat} (HB : has_bincoprod B) (b : B) : has_bincoprod (slice_bicat b). Proof. intros h₁ h₂. pose (sum := HB (pr1 h₁) (pr1 h₂)). refine (slice_coprod_cone b (pr2 h₁) (pr2 h₂) _ _ _ (pr2 sum) ,, _). split. - apply (slice_coprod_ump_1 b (pr2 h₁) (pr2 h₂)). - apply (slice_coprod_ump_2 b (pr2 h₁) (pr2 h₂)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. 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.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Slice. Require Import UniMath.Bicategories.Colimits.Initial. Require Import UniMath.Bicategories.Colimits.Coproducts.