Definition disp_cell_unit_bicat_adjoint_equivalent {a b : C} (f : adjoint_equivalence a b) (aa : disp_cell_unit_bicat a) (bb : disp_cell_unit_bicat b) : (aa -->[ f] bb × bb -->[ left_adjoint_right_adjoint f] aa) ≃ disp_adjoint_equivalence f aa bb. Proof. use weqfibtototal ; cbn. intro. apply disp_cell_unit_bicat_left_adjoint_equivalence_weq. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.Initial. Require Import UniMath.Bicategories.Core.Examples.Final. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.