Group-2-groupoids and 2G-crossed modules

Alemdar N., Temel S.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.48, no.5, pp.1388-1397, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 5
  • Publication Date: 2019
  • Doi Number: 10.15672/hjms.2018.580
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1388-1397
  • Keywords: group-2-groupoid, 2G-crossed module, CROSSED-MODULES, GROUPOIDS
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

In this paper, we introduce the notion of a group-2-groupoid as a group object in the category of 2-groupoids. We also obtain a 2G-crossed module by using the structure of a group-2-groupoid. Then we prove that the category GP2GD of group-2-groupoids and the category 2GXMoD of 2G-crossed modules are equivalent.