Definition preserves_runitor {C D : category} {F : functor C D} {tuC : tensor_unit C} {tuD : tensor_unit D} (ptuF : functor_tensor_unit tuC tuD F) (ruC : runitor tuC) (ruD : runitor tuD) : UU := ∏ x : C, ((identity (F x)) ⊗^{tuD} pu_{ptuF}) · (pr1 pt_{ptuF} x I_{tuC}) · (functor_on_morphisms F (pr1 ruC x)) = pr1 ruD (F x).
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.