Liftings of Crossed Modules in the Category of Groups with Operations

Akiz H. F., MUCUK O., Sahan T.

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, cilt.38, sa.7, ss.181-193, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 7
  • Basım Tarihi: 2020
  • Doi Numarası: 10.5269/bspm.v38i7.46500
  • Dergi Adı: BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.181-193
  • Erciyes Üniversitesi Adresli: Evet

Özet

In this paper we define the notion of lifting of a crossed module via the morphism in groups with operations and give some properties of this type of liftings. Further we prove that the lifting crossed modules of a certain crossed module are categorically equivalent to the internal groupoid actions on groups with operations, where the internal groupoid corresponds to the crossed module.