Definition disp_leftunitor_nat {C : category} {D : disp_cat C} {M : monoidal C} {DT : disp_tensor D M} {i : D I_{M}} (dlu : disp_leftunitor_data DT i) : UU := ∏ (x y : C) (f : C⟦x,y⟧) (xx : D x) (yy : D y) (ff : xx -->[f] yy), (i ⊗⊗^{DT}_{l} ff) ;; (dlu y yy) = transportb _ (pr1 (monoidal_leftunitorlaw M) _ _ _) (dlu x xx ;; ff).
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.