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