Definition enriched_profunctor_transformation_laws {V : sym_mon_closed_cat} {C₁ C₂ : category} {E₁ : enrichment C₁ V} {E₂ : enrichment C₂ V} {P Q : E₁ ↛e E₂} (τ : enriched_profunctor_transformation_data P Q) : UU := (∏ (x₁ x₂ : C₂) (y : C₁), identity (E₂ ⦃ x₂, x₁ ⦄) #⊗ τ x₁ y · lmap_e Q x₁ x₂ y = lmap_e P x₁ x₂ y · τ x₂ y) × (∏ (x : C₂) (y₁ y₂ : C₁), identity (E₁ ⦃ y₁, y₂ ⦄) #⊗ τ x y₁ · rmap_e Q x y₁ y₂ = rmap_e P x y₁ y₂ · τ x y₂).
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.CurriedBifunctors. Require Import UniMath.CategoryTheory.EnrichedCats.Bifunctors.CurriedTransformations. Require Import UniMath.CategoryTheory.EnrichedCats.Bifunctors.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.EnrichedCats.Bifunctors.WhiskeredTransformations. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.OppositeEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Profunctor. 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.