Proposition enriched_profunctor_whiskered_bifunctor_weq_right (P : E₁ ↛e E₂) : enriched_whiskered_bifunctor_to_profunctor (enriched_profunctor_to_whiskered P) = P. Proof. use subtypePath. { intro. apply isaprop_enriched_profunctor_laws. } refine (maponpaths (λ z, pr11 P ,, z) _). use pathsdirprod. - use funextsec ; intro x₁. use funextsec ; intro x₂. use funextsec ; intro y ; cbn. apply internal_beta. - use funextsec ; intro x₁. use funextsec ; intro x₂. use funextsec ; intro y ; cbn. apply internal_beta. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.Enriched.Enriched. Require Import UniMath.CategoryTheory.EnrichedCats.Enriched.EnrichmentEquiv. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.Tensor. Require Import UniMath.CategoryTheory.EnrichedCats.Bifunctors.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.OppositeEnriched. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Import MonoidalNotations. Section FromEnrichedProfunctor. End FromEnrichedProfunctor.