Crossed squares, crossed modules over groupoids and cat<SUP>1-2</SUP>-groupoids


TEMEL S.

CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, cilt.13, sa.1, ss.125-141, 2020 (ESCI, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 1
  • Basım Tarihi: 2020
  • Dergi Adı: CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.125-141
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

The aim of this paper is to introduce the notion of cat(1)-groupoids which are the groupoid version of cat(1)-groups and to prove the categorical equivalence between crossed modules over groupoids and cat(1)-groupoids. In section 4 we introduce the notions of crossed squares over groupoids and of cat(2)-groupoids, and then we show their categories are equivalent. These equivalences enable us to obtain more examples of groupoids.