Definition cmonoidal_to_noncurried_nattrans (M N : UMONCAT) {F G : LaxMonoidalFunctorCat (pr1 (cmonoidal_to_noncurriedmonoidal M)) (pr1 (cmonoidal_to_noncurriedmonoidal N))} (α : LaxMonoidalFunctorCat (pr1 (cmonoidal_to_noncurriedmonoidal M)) (pr1 (cmonoidal_to_noncurriedmonoidal N)) ⟦ F, G ⟧) : (hom M N)⟦ (λ F0 : LaxMonoidalFunctorCat (pr1 (cmonoidal_to_noncurriedmonoidal M)) (pr1 (cmonoidal_to_noncurriedmonoidal N)), cmonoidal_to_noncurried_functor M N F0) F, (λ F0 : LaxMonoidalFunctorCat (pr1 (cmonoidal_to_noncurriedmonoidal M)) (pr1 (cmonoidal_to_noncurriedmonoidal N)), cmonoidal_to_noncurried_functor M N F0) G ⟧. Proof. exists (pr11 α). use tpair. - use tpair. + split. * intros x y. etrans. 2: { apply maponpaths_2. apply (! tensor_on_hom_eq N _ _). } exact (! pr121 α x y). * exact (pr221 α). + repeat split ; exact tt. - repeat split. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorCategory. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.EquivalenceWhiskeredNonCurriedMonoidalCategories. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesReordered. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.AssociatorUnitorsLayer. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.FinalLayer. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.AssociatorUnitorsLayer. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.FinalLayer. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.EquivalenceMonCatCurried. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.EquivalenceWhiskeredCurried.