Crossed squares, crossed modules over groupoids and cat1−2−groupoids

TEMEL S.

Categories and General Algebraic Structures with Applications, cilt.13, sa.1, ss.125-141, 2020 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.29252/cgasa.13.1.125
  • Dergi Adı: Categories and General Algebraic Structures with Applications
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.125-141
  • Anahtar Kelimeler: cat1−group, cat2−group, Crossed module, crossed square, groupoid
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

The aim of this paper is to introduce the notion of cat1−groupoids which are the groupoid version of cat1−groups and to prove the categorical equivalence between crossed modules over groupoids and cat1−groupoids. In section 4 we introduce the notions of crossed squares over groupoids and of cat2−groupoids, and then we show their categories are equivalent. These equivalences enable us to obtain more examples of groupoids.