Definition associator_nat {C : category} {tu : tensor_unit C} (α : associator_data tu) : UU := ∏ (x x' y y' z z' : C), ∏ (f : C⟦x,x'⟧) (g : C⟦y,y'⟧) (h : C⟦z,z'⟧), (α x y z)· (f ⊗^{tu} (g ⊗^{tu} h)) = ((f ⊗^{tu} g) ⊗^{tu} h) · (α x' y' z').
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. Import TensorNotation. Import TensorUnitNotation. Import TensorNotation. Import TensorUnitNotation. Import TensorNotation. Import TensorUnitNotation. Import TensorNotation. Import TensorUnitNotation. Import UnitorsAssociatorNotation. Import TensorNotation. Import TensorUnitNotation. Import UnitorsAssociatorNotation.