Lemma tensor_on_hom_eq (M : ob UMONCAT) {x1 x2 y1 y2 : pr11 M} (f : (pr11 M)⟦x1,x2⟧) (g : (pr11 M)⟦y1,y2⟧) : tensor_on_hom (pr11 (pr112 M)) x1 x2 y1 y2 f g = # (pr121 (cmonoidal_to_noncurriedmonoidal M)) (f #, g). Proof. etrans. 2: { apply (tensor_comp (pr1 (pr112 M)) _ _ _ _ _ _ _ _ _ _). } rewrite id_right. now rewrite id_left. Qed.
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.