Singular extensions and the second cohomology categorical group

被引：0

作者：

Garzon, A. R. ^{[1
]}

机构：

[1] Univ Granada, Fac Ciencias, Dept Algebra, E-18071 Granada, Spain

来源：

JOURNAL OF HOMOTOPY AND RELATED STRUCTURES | 2017年 / 12卷 / 02期

关键词：

(Symmetric) categorical group; Categorical action; Non-functorial derivation; 2-exactness; Cohomology categorical group; Singular extension; CLASSIFYING-SPACES; SCHREIER THEORY; NERVES;

D O I：

10.1007/s40062-016-0135-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a classification of the 2-groupoid of singular extensions of categorical groups by means of a second cohomology categorical group, whose definition uses the notion of nerve of a categorical group. This second cohomology is, then, shown to be involved in a five term 2-exact sequence a la Hochschild-Serre which is associated with any essentially surjective homomorphism of categorical groups.

引用

页码：447 / 485

页数：39

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