Definition total_psfunctor_data (FFdata : disp_psfunctor_data) : psfunctor_data (total_bicat D₁) (total_bicat D₂). Proof. use make_psfunctor_data. - exact (λ x, (F (pr1 x),, FFdata _ (pr2 x))). - exact (λ x y f, (#F (pr1 f) ,, disp_psfunctor_mor FFdata (pr2 f))). - exact (λ x y f g α, (##F (pr1 α),, disp_psfunctor_cell FFdata (pr2 α))). - exact (λ x, iso_in_E_weq _ _ (psfunctor_id F (pr1 x),, disp_psfunctor_id FFdata (pr2 x))). - refine (λ x y z f g, iso_in_E_weq _ _ _). exact (psfunctor_comp F (pr1 f) (pr1 g),, disp_psfunctor_comp FFdata (pr2 f) (pr2 g)). Defined.
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.