Lemma constant_functor_fmonoidal_laxlaws : fmonoidal_laxlaws constant_functor_fmonoidal_data. Proof. repeat split ; (intro ; intros ; rewrite id_right). - rewrite (bifunctor_leftid V). apply id_left. - rewrite (bifunctor_rightid V). apply id_left. - apply pathsinv0, (monoid_to_assoc_law V m). - apply (monoid_to_unit_left_law V m). - apply (monoid_to_unit_right_law V m). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Import BifunctorNotations. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids. Import MonoidalNotations.