Definition disp_prod_functor_over_fixed_base_data : disp_functor_data F (D1 × D1')%disp_cat (D2 × D2')%disp_cat. Proof. exists (λ x, dirprodf (FF x) (FF' x)). intros x y xx yy f ff. exists (pr21 FF x y (pr1 xx) (pr1 yy) f (pr1 ff)). exact (pr21 FF' x y (pr2 xx) (pr2 yy) f (pr2 ff)). 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.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.