交叉模块局部化的可接受性

IF 0.6 4区 数学 Q3 MATHEMATICS
Olivia Monjon, Jérôme Scherer, Florence Sterck
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引用次数: 1

摘要

条件平坦性的概念与伽罗瓦意义上的容许性的对应关系,出现在任何半阿贝尔范畴中允许光纤局部化的局部化函子的情况下。那么很自然地想知道在光纤定位并不总是可用的交叉模块类别中会发生什么。在本文中,我们建立了正则-正则泛函子在伽罗瓦意义上的条件平坦性和可容许性之间的等价(对于正则泛函子类)。我们利用这个等价证明了即使它们的局部态的核不是无环的,对于正则泛型的类,无效函子是可容许的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Admissibility of Localizations of Crossed Modules

Admissibility of Localizations of Crossed Modules

The correspondence between the concept of conditional flatness and admissibility in the sense of Galois appears in the context of localization functors in any semi-abelian category admitting a fiberwise localization. It is then natural to wonder what happens in the category of crossed modules where fiberwise localization is not always available. In this article, we establish an equivalence between conditional flatness and admissibility in the sense of Galois (for the class of regular epimorphisms) for regular-epi localization functors. We use this equivalence to prove that nullification functors are admissible for the class of regular epimorphisms, even if the kernels of their localization morphisms are not acyclic.

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来源期刊
CiteScore
1.30
自引率
16.70%
发文量
29
审稿时长
>12 weeks
期刊介绍: Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant. Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.
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