Definition actegory_pentagon_identity {C : category} {A : action_data C} (aα : actor_data A) : UU := ∏ (w v v' : V) (z : C), ((α_{Mon_V} w v v') ⊗^{A}_{r} z) · (aα w (v ⊗_{Mon_V} v') z) · (w ⊗^{A}_{l} (aα v v' z)) = (aα (w⊗_{Mon_V} v) v' z) · (aα w v (v' ⊗_{A} 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.