Group-groupoid actions and liftings of crossed modules

被引：11

作者：

Mucuk, Osman ^{[1
]}

Sahan, Tuncar ^{[2
]}

机构：

[1] Erciyes Univ, Dept Math, Kayseri, Turkey

[2] Aksaray Univ, Dept Math, Aksaray, Turkey

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2019年 / 26卷 / 03期

关键词：

Group-groupoid; action groupoid; lifting crossed module; covering groupoid; TOPOLOGICAL-GROUPS; INTERNAL CATEGORIES; EXTENSIONS; COVERINGS; SPACES;

D O I：

10.1515/gmj-2018-0001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is to define the notion of lifting via a group morphism for a crossed module and give some properties of this type of liftings. Further, we obtain a criterion for a crossed module to have a lifting crossed module. We also prove that the category of the lifting crossed modules of a certain crossed module is equivalent to the category of group-groupoid actions on groups, where the group-groupoid corresponds to the crossed module.

引用

页码：437 / 447

页数：11