Definition make_disp_psfunctor_data (obFF : ∏ x:B₁, D₁ x → D₂ (F x)) (morFF : ∏ (x y : B₁) (f : B₁⟦x,y⟧) (xx : D₁ x) (yy : D₁ y), (xx -->[f] yy) → (obFF x xx -->[#F f] obFF y yy)) (cellFF : ∏ (x y : B₁) (f g : B₁⟦x,y⟧) (α : f ==> g) (xx : D₁ x) (yy : D₁ y) (ff : xx -->[f] yy) (gg : xx -->[g] yy), (ff ==>[α] gg) → (morFF x y f xx yy ff ==>[##F α] morFF x y g xx yy gg)) (disp_psfunctor_id : ∏ (x : B₁) (xx : D₁ x), disp_invertible_2cell (psfunctor_id F x) (id_disp (obFF x xx)) (morFF x x (id₁ x) xx xx (id_disp xx))) (disp_psfunctor_comp : ∏ (x y z : B₁) (f : x --> y) (g : y --> z) (xx : D₁ x) (yy : D₁ y) (zz : D₁ z) (ff : xx -->[f] yy) (gg : yy -->[g] zz), disp_invertible_2cell (psfunctor_comp F f g) (comp_disp (morFF x y f xx yy ff) (morFF y z g yy zz gg)) (morFF x z (f · g) xx zz (comp_disp ff gg))) : disp_psfunctor_data := (obFF,, morFF,, cellFF,, disp_psfunctor_id,, disp_psfunctor_comp).
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.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.DisplayedBicats.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.FiberCategory. 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. Import PseudoFunctor.Notations.