Definition is_linear_nat_trans {F G : functor C D} (Fl : lineator_lax Mon_V ActC ActD F) (Gl : lineator_lax Mon_V ActC ActD G)(ξ : F ⟹ G) : UU := ∏ (v : V) (x : C), Fl v x · ξ (v ⊗_{ActC} x) = v ⊗^{ActD}_{l} ξ x · Gl v 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. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegories. Require Import UniMath.CategoryTheory.coslicecat. Require Import UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects. Import BifunctorNotations. Import MonoidalNotations. Import ActegoryNotations.