Definition total_functor_data {C' C} {F} {D' : disp_cat C'} {D : disp_cat C} (FF : disp_functor F D' D) : functor_data (total_category D') (total_category D). Proof. use make_functor_data. - intros xx. exists (F (pr1 xx)). exact (FF _ (pr2 xx)). - intros xx yy ff. exists (# F (pr1 ff))%cat. exact (♯ FF (pr2 ff)). Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.AxiomOfChoice. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence.