Definition composite_functor_tensor_unit {C D E : category} {F : functor C D} {G : functor D E} {tuC : tensor_unit C} {tuD : tensor_unit D} {tuE : tensor_unit E} (ptuF : functor_tensor_unit tuC tuD F) (ptuG : functor_tensor_unit tuD tuE G) : functor_tensor_unit tuC tuE (functor_composite F G). Proof. use tpair. - apply (compositions_preserves_tensor ptuF ptuG). - apply (composition_preserves_unit ptuF ptuG). Defined.
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.