Definition left_adjoint_data_disp_to_total {a b : B} {aa : D a} {bb : D b} {f : a --> b} (ff : aa -->[f] bb) : (∑ (α : left_adjoint_data f), disp_left_adjoint_data α ff) → @left_adjoint_data E (a,,aa) (b,,bb) (f,,ff). Proof. intros j'. pose (j := pr1 j'). pose (jj := pr2 j'). pose (g := left_adjoint_right_adjoint j). pose (gg := (disp_left_adjoint_right_adjoint _ jj : bb -->[g] aa)). use tpair. - exact (g,, gg). - simpl. use tpair. + use tpair; simpl. * apply (left_adjoint_unit j). * apply (disp_left_adjoint_unit _ jj). + use tpair; simpl. * apply (left_adjoint_counit j). * apply (disp_left_adjoint_counit _ jj). 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.