Definition make_disp_psfunctor {F : psfunctor B₁ B₂} (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), id_disp (obFF x xx) ==>[ psfunctor_id F x ] 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), (comp_disp (morFF x y f xx yy ff) (morFF y z g yy zz gg)) ==>[ psfunctor_comp F f g ] morFF x z (f · g) xx zz (comp_disp ff gg)) : disp_psfunctor D₁ D₂ F. Proof. use tpair. - use make_disp_psfunctor_data. + exact obFF. + exact morFF. + exact cellFF. + intros. use tpair. * apply disp_psfunctor_id. * apply HD₂. + intros. use tpair. * apply disp_psfunctor_comp. * apply HD₂. - abstract (repeat split; intro; intros; apply HD₁). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Biequivalence. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Modifications.Modification. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor. Require Import UniMath.Bicategories.DisplayedBicats.DispTransformation. Require Import UniMath.Bicategories.DisplayedBicats.DispModification.