Group-groupoid actions and liftings of crossed modules

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MUCUK O., Sahan T.

GEORGIAN MATHEMATICAL JOURNAL, vol.26, no.3, pp.437-447, 2019 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.1515/gmj-2018-0001
  • Journal Name: GEORGIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.437-447
  • Erciyes University Affiliated: Yes

Abstract

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.