Definition disp_pentagon_identity {C : category} {D : disp_cat C} {M : monoidal C} {DT : disp_tensor D M} (dα : disp_associator_data DT) : UU := ∏ (w x y z : C) (ww : D w) (xx : D x) (yy : D y) (zz : D z), ((dα _ _ _ ww xx yy) ⊗⊗^{DT}_{r} zz) ;; (dα _ _ _ ww (xx ⊗⊗_{DT} yy) zz) ;; (ww ⊗⊗^{DT}_{l} (dα _ _ _ xx yy zz)) = transportb _ ((monoidal_pentagonidentity M) w x y z) ((dα _ _ _ (ww ⊗⊗_{DT} xx) yy zz) ;; (dα _ _ _ ww xx (yy ⊗⊗_{DT} zz))).
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.