Equivalence of the categories of categorical groups and cssc-crossed modules

Datuashvili T., MUCUK O., ALEMDAR N., Şahan T.

Advanced Studies: Euro-Tbilisi Mathematical Journal, cilt.19, sa.1, ss.109-130, 2026 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.32513/asetmj/193220082619108
  • Dergi Adı: Advanced Studies: Euro-Tbilisi Mathematical Journal
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.109-130
  • Anahtar Kelimeler: c-crossed module, categorical group, cssc-crossed module, Group up to congruence relation
  • Erciyes Üniversitesi Adresli: Evet

Özet

In [8] we proved that any categorical group defines a c-crossed module, which is a cssc-crossed module defined in the same paper. In [9] we constructed a categorical group for any cssc-crossed module. In the presented paper we prove that these correspondences define functors between the corresponding categories, which realize an equivalence of the categories of categorical groups and cssc-crossed modules.