Definition preservestensor_commutes {C D : category} {TC : tensor C} {TD : tensor D} {F G : functor C D} (ptF : preserves_tensor_data TC TD F) (ptG : preserves_tensor_data TC TD G) (α : nat_trans F G) : UU := ∏ (x y : C), (ptF x y) · α (x ⊗_{TC} y) = (α x) ⊗^{TD} (α y) · (ptG x y).
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.