A_infty$类的同调理论

arXiv - MATH - Category Theory Pub Date : 2024-08-09 DOI:arxiv-2408.05325

Mattia Ornaghi

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摘要

在本文中，我们描述了$A_\infty$范畴的同调范畴。为此，我们引入了半自由$A_\infty$范畴的概念，它扮演着标准同调的角色。此外，我们还定义了具有共振动态的非空$A_infty$（resp. DG）范畴，并证明了任何非空$A_infty$（resp. DG）范畴都有一个这样的解析。

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The Homotopy Theory of $A_\infty$Categories

In this paper we describe the homotopy category of the $A_\infty$categories. To do that we introduce the notion of semi-free $A_\infty$category, which plays the role of standard cofibration. Moreover, we define the non unital $A_\infty$ (resp. DG)categories with cofibrant morphisms and we prove that any non unital $A_\infty$ (resp. DG)category has a resolution of this kind.

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arXiv - MATH - Category Theory

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