Definition smash_product_monoidal_data : monoidal_data (category_of_hset_struct P). Proof. use make_monoidal_data. - exact smash_product_tensor_data. - exact (hset_struct_with_smash_closed_unit P). - exact hset_struct_smash_prod_lunitor. - exact hset_struct_smash_prod_linvunitor. - exact hset_struct_smash_prod_runitor. - exact hset_struct_smash_prod_rinvunitor. - exact hset_struct_smash_prod_lassociator. - exact hset_struct_smash_prod_rassociator. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructuresSmashProduct. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Terminal.