Lemma strictlytensorpreserving_is_strong {C D : category} {M : monoidal C} {N : monoidal D} {F : functor C D} {pt : preserves_tensordata M N F} (pst : preserves_tensor_strictly pt) : preserves_tensor_strongly pt. Proof. intros x y. use (iso_stable_under_equalitytransportf (pr2 (pst x y)) (is_z_isomorphism_identity (F x ⊗_{N} F y))). 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.