Definition preserves_tensor_nat_left {C D : category} {M : monoidal C} {N : monoidal D} {F : functor C D} (pt : preserves_tensordata M N F) : UU := ∏ (x y1 y2 : C) (g : C⟦y1,y2⟧), F x ⊗^{ N}_{l} # F g · pt x y2 = pt x y1 · # F (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.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import BifunctorNotations. Import MonoidalNotations.