论文标题
NDG类别的派生类别
Derived categories of NDG categories
论文作者
论文摘要
我们研究$ n $ -Differential分级（$ NDG $）类别及其派生类别。首先，我们在$ ndg $类别$ \ mathcal {a} $上引入$ n $ -differential模块。然后，我们表明类别$ \ MathSf {C} _ {ndg}（\ Mathcal {a}）$ $ n $ -divferential $ \ Mathcal {a} $ - 模块是Frobenius类别三角类别。其次，我们研究了派生类别的属性$ \ mathsf {d} _ {ndg}（\ Mathcal {a}）$，并在$ NDG $类别的派生类别之间给出Morita类型的三角形等价。最后，我们显示$ \ mathsf {d} _ {ndg}（\ Mathcal {a}）$是三角形，等于某些普通DG类别的派生类别。
We study $N$-differential graded ($NDG$) categories and their the derived categories. First, we introduce $N$-differential modules over an $NDG$ category $\mathcal{A}$. Then we show that the category $\mathsf{C}_{Ndg}(\mathcal{A})$ of $N$-differential $\mathcal{A}$-modules is a Frobenius category, and that its homotopy category $\mathsf{K}_{Ndg}(\mathcal{a})$ is a triangulated category. Second, we study the properties of the derived category $\mathsf{D}_{Ndg}(\mathcal{A})$ and give triangle equivalences of Morita type between derived categories of $NDG$ categories. Finally, we show $\mathsf{D}_{Ndg}(\mathcal{A})$ is triangle equivalent to the derived category of some ordinary DG category.
