Definition make_enrichment_over_smash_struct_data : enrichment_data C (smash_product_monoidal_cat P). Proof. simple refine (_ ,, _ ,, _ ,, _ ,, _). - exact (λ x y, _ ,, SC x y). - refine (λ x, pointed_hset_struct_map_from_unit P (SC x x) (identity _) ,, _). abstract (cbn ; apply hset_struct_with_smash_map_from_unit). - simple refine (λ x y z, _ ,, _). + exact smash_struct_comp. + use hset_struct_with_smash_map_from_smash. apply smash_struct_enrichment_comp. - refine (λ x y f, pointed_hset_struct_map_from_unit P (SC x y) f ,, _). abstract (cbn ; apply hset_struct_with_smash_map_from_unit). - exact (λ x y f, pr1 f true). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. 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.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Examples.SmashProductMonoidal. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Section FromStructSmashEnrichment. End FromStructSmashEnrichment.