Lemma tensorialstrength_preserves_actor {C : category} (M : monoidal C) {F : functor C C} (ts : tensorialstrength M F) : preserves_actor _ _ _ _ ts = ∏ v w x : C, ts (v ⊗_{M} w) x · # F α^{M}_{v, w, x} = α^{M}_{v, w, F x} · v ⊗^{M}_{l} ts w x · ts v (w ⊗_{M} x). Proof. apply idpath. 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.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegories. Require Import UniMath.CategoryTheory.coslicecat. Require Import UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects. Import BifunctorNotations. Import MonoidalNotations. Import ActegoryNotations.