Augmentation categories in higher dimensions

For an exact symplectic manifold $M$ and a Legendrian submanifold $\mathrm{\Lambda }$ of the contactification $M\times \mathbb{R}$, we construct the augmentation category (over a field of characteristic 2), a unital $A_{\mathrm{\infty }}$-category whose objects are augmentations of the Chekanov-Eliashberg differential graded algebra. This extends the construction of the augmentation category by Ng-Rutherford-Shende-Sivek-Zaslow to contact manifolds of dimension greater than 3.