Definition mor_weq_enriched_smash_hom (x y : C) : pr11 (E ⦃ x , y ⦄) ≃ (x --> y). Proof. use weq_iso. - exact enriched_smash_hom_to_mor. - exact mor_to_enriched_smash_hom. - abstract (intro f ; unfold mor_to_enriched_smash_hom, enriched_smash_hom_to_mor ; rewrite enriched_from_to_arr ; apply idpath). - abstract (intro f ; unfold mor_to_enriched_smash_hom, enriched_smash_hom_to_mor ; refine (_ @ enriched_to_from_arr E f) ; apply maponpaths ; use eq_mor_hset_struct ; intro b ; cbn ; induction b ; [ apply idpath | ] ; cbn ; rewrite <- (pointed_hset_struct_preserve_point _ (pr2 (enriched_from_arr E f))) ; apply maponpaths ; apply hset_struct_with_smash_point_unit). 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.