关于微分等级范畴与 A 无穷范畴之间等价性的评论

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2024-05-01 DOI:10.4310/hha.2024.v26.n1.a17

James Pascaleff

引用次数: 0

摘要

我们证明了在一个域上的微分级数范畴和 $A_\infty$ 范畴的同调理论在 $(\infty, 1)$ 范畴的层面上是等价的。这些结果是卡诺纳科-奥纳吉-斯特拉利（Canonaco-Ornaghi-Stellari）定理与不同版本的$(\infty, 1)$类之间的一般关系相结合的推论。

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Remarks on the equivalence between differential graded categories and A-infinity categories

We show that the homotopy theories of differential graded categories and $A_\infty$-categories over a field are equivalent at the $(\infty, 1)$-categorical level. The results are corollaries of a theorem of Canonaco–Ornaghi–Stellari combined with general relationships between different versions of $(\infty, 1)$-categories.

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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.