Definition preserves_tensor_data {C D : category} (TC : tensor_data C) (TD : tensor_data D) (F : functor C D) : UU := ∏ (x y : C), D ⟦ F x ⊗_{TD} F y, F (x ⊗_{TC} 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.