Definition identity_fmonoidal_stronglaws {C : category} (M : monoidal C) : fmonoidal_stronglaws (fmonoidal_preservestensordata (identity_fmonoidal_lax M)) (fmonoidal_preservesunit (identity_fmonoidal_lax M)). Proof. split. - intros x y. apply is_z_isomorphism_identity. - apply is_z_isomorphism_identity. Defined.
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.