On the topological generalized crossed modules


Gürsoy M. H.

ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES, vol.48, no.2, pp.183-193, 2021 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 2
  • Publication Date: 2021
  • Journal Name: ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Page Numbers: pp.183-193
  • Keywords: Topological group, topological generalized group, generalized action, crossed module, generalized crossed module, generalized group-groupoid
  • Inonu University Affiliated: Yes

Abstract

In this paper, we define the topological versions of the concepts of crossed module over generalized groups, which is called generalized crossed module, and generalized group-groupoid. We construct the categories of the topological generalized crossed modules and their homomorphisms and of the topological generalized group-groupoid and homomorphisms between them. We also obtain some characterizations related to the concepts of topological generalized crossed module and topological generalized group-groupoid. Finally, at the end of the work, we prove that the category of topological generalized crossed modules is equivalent to that of topological generalized group-groupoids whose object sets are commutative topological generalized groups.