Definition disp_cell_unit_bicat_left_adjoint_equivalence {a b : C} (f : adjoint_equivalence a b) {aa : disp_cell_unit_bicat a} {bb : disp_cell_unit_bicat b} (ff : aa -->[ f] bb) : bb -->[ left_adjoint_right_adjoint f] aa → disp_left_adjoint_equivalence f ff. Proof. intros gg. use tpair. - use tpair. + exact gg. + exact (tt ,, tt). - split ; split ; cbn. + apply isapropunit. + apply isapropunit. + exact (disp_cell_unit_bicat_is_disp_invertible_2cell (left_adjoint_unit f ,, _) tt). + exact (disp_cell_unit_bicat_is_disp_invertible_2cell (left_adjoint_counit f ,, _) tt). 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.