Derived categories of NDG categories

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2021-03-31 DOI:10.1007/s40062-021-00279-3

Jun-ichi Miyachi, Hiroshi Nagase

引用次数: 0

Abstract

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.

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NDG类别的衍生类别

本文研究了n个微分分级范畴及其派生范畴。首先，我们引入n阶微分分级范畴上的模。然后我们证明了它们构成了一个Frobenius范畴，并且它的同伦范畴是三角化的。其次，研究了其派生范畴的性质，给出了n个微分分级范畴的派生范畴之间的Morita型三角等价。最后，我们证明了该派生范畴与某常微分分级范畴的派生范畴是三角等价的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.