Definition biinitial_1cell_property_slice : biinitial_1cell_property κ. Proof. intros f. refine (is_biinitial_1cell_property (pr2 I) _ ,, _) ; cbn. apply (is_biinitial_invertible_2cell_property (pr2 I)). 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.