Definition one_types : bicat. Proof. use build_bicategory. - exact one_type_bicat_data. - exact one_type_bicat_laws. - intros X Y f g ; cbn in *. apply (impred 2 (λ x, f x = g x)). exact (λ x, pr2 Y (f x) (g x)). Defined.
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.Univalence. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique.