Proposition enrichment_over_struct_weq_struct_enrichment_inv_2 {C : category} (E : struct_enrichment C) : make_struct_enrichment C (make_enrichment_over_struct C E) = E. Proof. use subtypePath. { intro. apply isaprop_struct_enrichment_laws. } use funextsec ; intro x. use funextsec ; intro y. simpl. unfold make_struct_enrichment_data. unfold make_enrichment_over_struct. simpl. unfold transportf_struct_weq. refine (_ @ idpath_transportf _ _). apply maponpaths_2. refine (_ @ univalence_hSet_idweq _). apply maponpaths. use subtypePath. { intro ; apply isapropisweq. } apply idpath. Qed.
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.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Examples.StructuresMonoidal. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Section FromStructEnrichment. End FromStructEnrichment.