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.

中文翻译：

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N DG类别的派生类别

在本文中，我们研究了N-微分分级类别及其派生类别。首先，我们介绍N级差异分类类别的模块。然后，我们证明它们构成了Frobenius类别，并且其同伦类别是三角划分的。其次，我们研究其派生类别的性质，并给出N微分等级类别的派生类别之间Morita类型的三角形等价性。最后，我们证明此派生类别是三角形的，等效于某些常微分渐变类别的派生类别。