Covering morphisms of topological internal groupoids


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MUCUK O., AKIZ H. F.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.49, no.3, pp.1020-1029, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.15672/hujms.467559
  • Title of Journal : HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Page Numbers: pp.1020-1029

Abstract

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.