Definition actor_nat_leftrightwhisker {C : category} {A : action_data C} (aα : actor_data A) : UU := ∏ (v w w' : V) (z : C) (g : V⟦w,w'⟧), (aα v w z) · (v ⊗^{A}_{l} (g ⊗^{A}_{r} z)) = ((v ⊗^{Mon_V}_{l} g) ⊗^{A}_{r} z) · (aα v w' z).
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Foundations.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.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import BifunctorNotations. Import MonoidalNotations. Section EquivalenceFromTensorWithUnit. Import MonoidalNotations. End EquivalenceFromTensorWithUnit. Import MonoidalNotations. Import ActegoryNotations.