Definition preserves_associativity {C D : category} {M : monoidal C} {N : monoidal D} {F : functor C D} (pt : preserves_tensordata M N F) : UU := ∏ (x y z : C), ((pt x y) ⊗^{N}_{r} (F z)) · (pt (x ⊗_{M} y) z) · (#F (α^{M}_{x,y,z})) = α^{N}_{F x, F y, F z} · ((F x) ⊗^{N}_{l} (pt y z)) · (pt x (y ⊗_{M} z)).
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.