Lemma identity_fmonoidal_laxlaws {C : category} (M : monoidal C) : fmonoidal_laxlaws (identity_fmonoidal_data M). Proof. repeat split; red; unfold fmonoidal_preservesunit, fmonoidal_preservestensordata; cbn; intros. - rewrite id_left. apply id_right. - rewrite id_left. apply id_right. - do 2 rewrite id_right. rewrite (bifunctor_rightid M). rewrite (bifunctor_leftid M). rewrite id_right. apply id_left. - rewrite id_right. rewrite (bifunctor_rightid M). apply id_left. - rewrite id_right. rewrite (bifunctor_leftid M). apply id_left. 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.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import BifunctorNotations. Import MonoidalNotations.