Lemma is_precategory_data_from_prebicat_and_ob: is_precategory precategory_data_from_bicat_and_ob. Proof. use make_is_precategory. - intros a b f; apply id2_left. - intros a b f; apply id2_right. - intros a b c d f g h; apply vassocr. - intros a b c d f g h; apply pathsinv0; apply vassocr. Qed.
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.