Definition smash_struct_comp {x y z : C} : setquot (smash_eqrel (pr1 P) (pr12 P) (SC y z) (SC x y)) → homset x z. Proof. use map_from_smash. - exact (λ f g, g · f). - abstract (intros f₁ f₂ ; cbn ; rewrite !(smash_struct_enrichment_comp_point_l SC) ; apply idpath). - abstract (intros g f ; cbn ; rewrite !(smash_struct_enrichment_comp_point_l SC) ; rewrite !(smash_struct_enrichment_comp_point_r SC) ; apply idpath). - abstract (intros g₁ g₂ ; cbn ; rewrite !(smash_struct_enrichment_comp_point_r SC) ; apply idpath). 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.