Definition total_tensor_data {C : category} {D : disp_cat C} {M : monoidal C} (DT : disp_tensor D M) : bifunctor_data T(D) T(D) T(D). Proof. use make_bifunctor_data. - intros x y. exact (pr1 x ⊗_{M} pr1 y ,, pr2 x ⊗⊗_{DT} pr2 y). - intros x y1 y2 g. exact (pr1 x ⊗^{M}_{l} pr1 g ,, pr2 x ⊗⊗^{DT}_{l} pr2 g). - intros y x1 x2 f. exact (pr1 f ⊗^{M}_{r} pr1 y ,, pr2 f ⊗⊗^{DT}_{r} pr2 y). 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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.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. Import BifunctorNotations. Import MonoidalNotations. Import DisplayedBifunctorNotations. Import DisplayedMonoidalNotations.