COVERING GROUPOIDS OF CATEGORICAL GROUPS

MUCUK O., Şahan T.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.42, sa.4, ss.419-430, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 4
  • Basım Tarihi: 2013
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.419-430
  • Erciyes Üniversitesi Adresli: Evet

Özet

If X is a topological group, then its fundamental groupoid pi(1)(X) is a group-groupoid which is a group object in the category of groupoids. Further if X is a path connected topological group which has a simply connected cover, then the category of covering groups of X and the category of covering groupoids of pi(1)(X) are equivalent. In this paper we prove that if (X, x(0)) is an H-group, then the fundamental groupoid pi(1)(X) is a weak categorical group. This enables one to prove that the category of the covering spaces of an H-group (X, x(0)) is equivalent to the category of covering groupoids of the weak categorical group pi(1)(X).