Definition comp_functor_unitors_associator {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} {uaC : unitors_associator tuC} {uaD : unitors_associator tuD} {uaE : unitors_associator tuE} (puaF : functor_unitors_associator uaC uaD ptuF) (puaG : functor_unitors_associator uaD uaE ptuG) : functor_unitors_associator uaC uaE (composite_functor_tensor_unit ptuF ptuG). Proof. repeat split. - apply (comp_preserves_lunitor puaF puaG). - apply (comp_preserves_runitor puaF puaG). - apply (comp_preserves_associator puaF puaG). 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.