Definition disp_associator_nat_leftwhisker {C : category} {D : disp_cat C} {M : monoidal C} {DT : disp_tensor D M} (dα : disp_associator_data DT) : UU := ∏ (x y z1 z2 : C) (h : C⟦z1,z2⟧) (xx : D x) (yy : D y) (zz1 : D z1) (zz2 : D z2) (hh : zz1-->[h] zz2), (dα _ _ _ xx yy zz1) ;; (xx ⊗⊗^{DT}_{l} (yy ⊗⊗^{DT}_{l} hh)) = transportb _ ((associatorlaw_natleft (monoidal_associatorlaw M)) x y z1 z2 h) (((xx ⊗⊗_{DT} yy) ⊗⊗^{DT}_{l} hh) ;; (dα _ _ _ xx yy zz2)).
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.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Projection. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Import MonoidalNotations. Import DisplayedBifunctorNotations.