Definition disp_psfunctor_iso {B₁ B₂ : bicat} {F : psfunctor B₁ B₂} {D₁ : disp_bicat B₁} {D₂ : disp_bicat B₂} (FF : disp_psfunctor D₁ D₂ F) : UU := (∏ (x : B₁), isweq (FF x)) × (∏ (x y : B₁) (f : x --> y) (xx : D₁ x) (yy : D₁ y), isweq (λ (ff : xx -->[ f ] yy), disp_psfunctor_mor _ _ _ FF ff)) × (∏ (x y : B₁) (f g : x --> y) (τ : f ==> g) (xx : D₁ x) (yy : D₁ y) (ff : xx -->[ f ] yy) (gg : xx -->[ g ] yy), isweq (λ (ττ : ff ==>[ τ ] gg), disp_psfunctor_cell _ _ _ FF ττ)).
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.Examples.Initial. Require Import UniMath.Bicategories.Core.Examples.Final. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor. Require Import UniMath.Bicategories.DisplayedBicats.DispTransportLaws.