Lemma path_internal_adjoint_equivalence {C : bicat} {X Y : C} (HC : is_univalent_2_1 C) (A₁ A₂ : adjoint_equivalence X Y) (H : arrow_of_adjunction A₁ = A₂) : A₁ = A₂. Proof. use total2_paths_f. - exact H. - apply unique_internal_adjoint_equivalence. apply HC. Qed.
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.