Definition total_monoidaldata {C : category} {D : disp_cat C} {M : monoidal C} (DM : disp_monoidal_data D M) : monoidal_data T(D). Proof. use make_monoidal_data. - exact (total_tensor_data DM). - exact (total_unit DM dI_{DM}). - exact (total_leftunitordata dlu^{DM}). - exact (total_leftunitorinvdata dluinv^{DM}). - exact (total_rightunitordata dru^{DM}). - exact (total_rightunitorinvdata druinv^{DM}). - exact (total_associatordata dα^{DM}). - exact (total_associatorinvdata dαinv^{DM}). 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.