Covering morphisms of topological internal groupoids

MUCUK O., Akiz H. F.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.49, sa.3, ss.1020-1029, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.15672/hujms.467559
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1020-1029
  • Erciyes Üniversitesi Adresli: Evet

Özet

Let X be a topological group with operations whose underlying space has a universal cover. Then the fundamental groupoid pi X becomes a topological internal groupoid, i.e., an internal groupoid in the category of topological groups. In this paper, we prove that the slice category Cov(sTC)/X of covering morphisms p: (X) over tilde -> X of topological groups with operations in which (X) over tilde has also a universal cover and the category Cov(Gpd(TC))/pi X of covering morphisms q : (G) over tilde -> pi X of topological internal groupoids based on pi X are equivalent. We also prove that for a topological internal groupoid G, the category Cov(Gpd(TC))/G of covering morphisms of topological internal groupoids based on G and the category Act(Gpd(TC))/G of topological internal groupoid actions of G on topological groups with operations are equivalent.