Definition associator_nat_leftrightwhisker {C : category} {T : tensor_data C} (α : associator_data T) : UU := ∏ (x y y' z : C) (g : C⟦y,y'⟧), (α x y z) · (x ⊗^{ T}_{l} (g ⊗^{ T}_{r} z)) = ((x ⊗^{ T}_{l} g) ⊗^{ T}_{r} z) · (α x y' z).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.MoreFoundations.PartA. 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.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.opp_precat. Import BifunctorNotations. Import MonoidalNotations. Section EquivalenceFromTensorWithUnit. Import MonoidalNotations. End EquivalenceFromTensorWithUnit. Import MonoidalNotations. Import MonoidalNotations. Import MonoidalNotations. Import MonoidalNotations. Import MonoidalNotations.