Definition section_functor_data : functor_data C (total_category D). Proof. exists (λ x, (x ,, sd x)). intros x y f. exists f. exact (section_disp_on_morphisms sd f). Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Reindexing.