Crossed Modules, Double Group-Groupoids and Crossed Squares

Temel S., Şahan T., Mucuk O.

FILOMAT, cilt.34, sa.6, ss.1755-1769, 2020 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 6
  • Basım Tarihi: 2020
  • Doi Numarası: 10.2298/fil2006755t
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.1755-1769
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

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.