Definition enriched_nat_trans_curried_weq {V : sym_monoidal_cat} {C₁ C₂ C₃ : category} {E₁ : enrichment C₁ V} {E₂ : enrichment C₂ V} {E₃ : enrichment C₃ V} (F G : enriched_curried_bifunctor E₁ E₂ E₃) : enriched_nat_trans (enriched_curried_bifunctor_to_bifunctor F) (enriched_curried_bifunctor_to_bifunctor G) ≃ curried_enriched_transformation F G. Proof. use weq_iso. - exact enriched_nat_trans_to_curried. - exact curried_enriched_transformation_to_nat_trans. - abstract (intros τ ; use subtypePath ; [ intro ; repeat (use impred ; intro) ; apply homset_property | ] ; use funextsec ; intro xy ; cbn ; apply enriched_from_to_arr). - abstract (intros τ ; use eq_curried_enriched_transformation ; intros x y ; cbn ; apply enriched_to_from_arr). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. 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.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import MonoidalNotations.