群的交叉模与对称上同调

arXiv: K-Theory and Homology Pub Date : 2019-02-05 DOI:10.4310/hha.2020.v22.n2.a7

Mariam Pirashvili

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引用次数: 3

摘要

本文将第三对称上同调(由Staic和Zarelua引入)与具有一定性质的交叉模联系起来。2群语言的等效结果表明，2群的扩展对应于$HS^3$的元素，如果它具有在2范畴意义上保留逆的区段。这与Staic(和Zarelua)关于$HS^2$和群的阿贝尔扩展的结果一致。

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Crossed modules and symmetric cohomology of groups

This paper links the third symmetric cohomology (introduced by Staic and Zarelua ) to crossed modules with certain properties. The equivalent result in the language of 2-groups states that an extension of 2-groups corresponds to an element of $HS^3$ iff it possesses a section which preserves inverses in the 2-categorical sense. This ties in with Staic's (and Zarelua's) result regarding $HS^2$ and abelian extensions of groups.

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arXiv: K-Theory and Homology

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