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Galois theory and the categorical Peiffer commutator
Homology, Homotopy and Applications ( IF 0.5 ) Pub Date : 2020-01-01 , DOI: 10.4310/hha.2020.v22.n2.a20
Alan S. Cigoli 1 , Arnaud Duvieusart 1 , Marino Gran 1 , Sandra Mantovani 2
Affiliation  

We show that the Peiffer commutator previously defined by Cigoli, Mantovani and Metere can be used to characterize central extensions of precrossed modules with respect to the subcategory of crossed modules in any semi-abelian category satisfying an additional property. We prove that this commutator also characterizes double central extensions, obtaining then some Hopf formulas for the second and third homology objects of internal precrossed modules.

中文翻译:

伽罗瓦理论和分类 Peiffer 换向器

我们表明,先前由 Cigoli、Mantovani 和 Metere 定义的 Peiffer 换向器可用于表征预交叉模块的中心扩展,该中心扩展相对于满足附加属性的任何半阿贝尔类别中的交叉模块的子类别。我们证明这个交换子也表征了双中心扩展,然后获得了内部预交叉模块的第二个和第三个同源对象的一些 Hopf 公式。
更新日期:2020-01-01
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