Definition section_to_psfunctor_data : psfunctor_data B (total_bicat D). Proof. use make_psfunctor_data. - exact (λ x, x ,, section_on_ob s x). - exact (λ x y f, f ,, section_on_mor s f). - exact (λ x y f g τ, τ ,, section_on_cell s τ). - exact (λ x, id2 _ ,, pr1 (section_on_id s x)). - exact (λ x y z f g, id2 _ ,, pr1 (section_on_comp s f g)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor.