Definition fl_preserves_tensor_nat_left (spt : fl_preserves_tensor_data) : UU := ∏ (x y1 y2 : C') (g : C'⟦y1,y2⟧), sd x ⊗⊗^{DM}_{l} # sd g ;; spt x y2 = transportb _ (fmonoidal_preservestensornatleft Fm x y1 y2 g) (spt x y1 ;; # sd (x ⊗^{M'}_{l} g)).
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.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Import BifunctorNotations. Import MonoidalNotations. Import DisplayedBifunctorNotations. Import DisplayedMonoidalNotations.