Crossed Modules, Double Group-Groupoids and Crossed Squares

Temel S., Şahan T., Mucuk O.

FILOMAT, vol.34, no.6, pp.1755-1769, 2020 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 34 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.2298/fil2006755t
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.1755-1769
  • Recep Tayyip Erdoğan University Affiliated: Yes


The purpose of this paper is to obtain the notion of crossed modules over group-groupoids considering split extensions and prove a categorical equivalence between these types of crossed modules and double group-groupoids. This equivalence enables us to produce various examples of double groupoids. We also prove that crossed modules over group-groupoids are equivalent to crossed squares.