Definition sigma_disp_cat_tensor_data : disp_bifunctor_data M (sigma_disp_cat E) (sigma_disp_cat E) (sigma_disp_cat E). Proof. simple refine (_ ,, (_ ,, _)). - intros x y [xx xxx] [yy yyy]. exists (xx ⊗⊗_{DM} yy). exact (xxx ⊗⊗_{EM} yyy). - intros x y1 y2 g [xx xxx] [yy1 yyy1] [yy2 yyy2] [gg ggg]. exists (xx ⊗⊗^{DM}_{l} gg). exact (xxx ⊗⊗^{EM}_{l} ggg). - intros y1 y2 x g [yy1 yyy1] [yy2 yyy2] [xx xxx] [gg ggg]. exists (gg ⊗⊗^{DM}_{r} xx). exact (ggg ⊗⊗^{EM}_{r} xxx). 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.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Projection. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Sigma. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import BifunctorNotations. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Examples.Fullsub. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import MonoidalNotations. Import DisplayedBifunctorNotations. Import DisplayedMonoidalNotations.