Definition tensor_from_bicat_and_ob: category_from_bicat_and_ob ⊠ category_from_bicat_and_ob ⟶ category_from_bicat_and_ob. Proof. use make_functor. - use make_functor_data. + intro ab. exact (pr1 ab · pr2 ab). + intros ab1 ab2 f. exact (hcomp (pr1 f) (pr2 f)). - abstract ( split; [ intro c; apply hcomp_identity | intros a b c f g; apply hcomp_vcomp ] ). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.Bicategories.Core.Bicat. Section Monoidal_Cat_From_Bicat. Import Bicat.Notations. End Monoidal_Cat_From_Bicat.