Definition preserves_lunitor {C D : category} {F : functor C D} {tuC : tensor_unit C} {tuD : tensor_unit D} (ptuF : functor_tensor_unit tuC tuD F) (luC : lunitor tuC) (luD : lunitor tuD) : UU := ∏ x : C, (pu_{ptuF} ⊗^{tuD} (identity (F x))) · (pr1 pt_{ptuF} I_{tuC} x) · (functor_on_morphisms F (pr1 luC x)) = pr1 luD (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.