Definition disp_is_biequivalence_data {F : psfunctor B₁ B₂} {G : psfunctor B₂ B₁} {e : is_biequivalence_unit_counit F G} (a : is_biequivalence_adjoints e) {FF : disp_psfunctor D₁ D₂ F} {GG : disp_psfunctor D₂ D₁ G} (ee : is_disp_biequivalence_unit_counit e FF GG) : UU := ∑ (uu : disp_pstrans (disp_pseudo_id D₁) (disp_pseudo_comp _ _ _ _ _ FF GG) (invunit_of_is_biequivalence a)) (cc : disp_pstrans (disp_pseudo_id D₂) (disp_pseudo_comp _ _ _ _ _ GG FF) (invcounit_of_is_biequivalence a)), (disp_invmodification _ _ _ _ (disp_comp_pstrans uu (unit_of_is_disp_biequivalence ee)) (disp_id_pstrans _) (unitcounit_of_is_biequivalence _) × disp_invmodification _ _ _ _ (disp_comp_pstrans (unit_of_is_disp_biequivalence ee) uu) (disp_id_pstrans _) (unitunit_of_is_biequivalence _)) × (disp_invmodification _ _ _ _ (disp_comp_pstrans cc (counit_of_is_disp_biequivalence ee)) (disp_id_pstrans _) (counitcounit_of_is_biequivalence _) × disp_invmodification _ _ _ _ (disp_comp_pstrans (counit_of_is_disp_biequivalence ee) cc) (disp_id_pstrans _) (counitunit_of_is_biequivalence _)).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. 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.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Require Import UniMath.Bicategories.PseudoFunctors.Biequivalence. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Modifications.Modification. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor. Require Import UniMath.Bicategories.DisplayedBicats.DispTransformation. Require Import UniMath.Bicategories.DisplayedBicats.DispModification. Import PseudoFunctor.Notations.