Derived categories of NDG categories

In this paper we study N-differential graded categories and their derived categories. First, we introduce modules over an N-differential graded category. Then we show that they form a Frobenius category and that its homotopy category is triangulated. Second, we study the properties of its derived category and give triangle equivalences of Morita type between derived categories of N-differential graded categories. Finally, we show that this derived category is triangle equivalent to the derived category of some ordinary differential graded category.