COVERING GROUPOIDS OF CATEGORICAL GROUPS


MUCUK O. , Şahan T.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.42, no.4, pp.419-430, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2013
  • Title of Journal : HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Page Numbers: pp.419-430

Abstract

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).