Definition internal_adjoint_equivalence_identity (a : C) : adjoint_equivalence a a. Proof. exists (identity a). use tpair. - apply internal_adjunction_data_identity. - split; [ apply is_internal_adjunction_identity |]. split. + apply is_invertible_2cell_linvunitor. + apply is_invertible_2cell_lunitor. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.BicategoryLaws.