Definition adjoint_unique_map_iso : is_invertible_2cell r₁_to_r₂. Proof. use tpair. - exact r₂_to_r₁. - cbn. split. + rewrite (composition_of_maps l A₁ A₂). apply composition_of_triangles_is_identity. + rewrite (composition_of_maps l A₂ A₁). apply composition_of_triangles_is_identity. 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.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv.