Definition left_adjoint_data_total_weq {a b : B} {aa : D a} {bb : D b} {f : a --> b} (ff : aa -->[f] bb) : @left_adjoint_data E (a,,aa) (b,,bb) (f,,ff) ≃ ∑ (α : left_adjoint_data f), disp_left_adjoint_data α ff. Proof. exists (left_adjoint_data_total_to_disp ff). use isweq_iso. - exact (left_adjoint_data_disp_to_total ff). - intro. reflexivity. - intro. reflexivity. 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.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.Core.Univalence.