Definition functor_strong {C D : category} {tuC : tensor_unit C} {tuD : tensor_unit D} {uaC : unitors_associator tuC} {uaD : unitors_associator tuD} {F : functor C D} {ptuF : functor_tensor_unit tuC tuD F} (puaF : functor_unitors_associator uaC uaD ptuF) : UU := is_z_isomorphism (pr2 ptuF) × ∏ x y : C, is_z_isomorphism (pr11 ptuF 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.