Definition empty_is_biinitial_one_types : is_biinitial empty_one_type. Proof. use make_is_biinitial. - exact (λ _, fromempty). - exact (λ _ _ _ z, fromempty z). - exact (λ _ _ _ _ _, funextsec _ _ _ (λ z, fromempty z)). Defined.
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.Examples.OneTypes. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.Examples.MorphismsInOneTypes. Require Import UniMath.Bicategories.Limits.CommaObjects. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.PullbackFunctions. Require Import UniMath.Bicategories.Limits.Examples.OneTypesLimits. Require Import UniMath.Bicategories.Colimits.Initial. Require Import UniMath.Bicategories.Colimits.Coproducts. Require Import UniMath.Bicategories.Colimits.Extensive.