模中拟范畴的变形

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI:10.1016/j.jpaa.2025.107866

Violeta Borges Marques, Wendy Lowen, Arne Mertens

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引用次数: 0

摘要

1990年，为了在丰富的情况下发展出更高的范畴概念，提出了范畴对象的框架。特别地，模中的拟范畴构成模的一个子类，根据[29]可以认为是一种“弱dg范畴（集中于同调正度）”。本文的主要目的是建立模子的变形理论。特别地，我们证明了模的准范畴在水平平面无穷小变形下是保持的。

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Deformations of quasi-categories in modules

The framework of templicial objects was put forth in [30] in order to develop higher categorical concepts in the presence of enrichment. In particular, quasi-categories in modules constitute a subclass of templicial modules which may be considered as a kind of “weak dg-categories (concentrated in homologically positive degrees)” according to [29]. The main goal of the present paper is to initiate the deformation theory of templicial modules. In particular, we show that quasi-categories in modules are preserved under levelwise flat infinitesimal deformation.

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来源期刊

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.