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CitationMucuk, O., Ay, H. Y. ve Bağrıyanık, B. (2009). Local Group-Groupoids. Maltepe Üniversitesi. s. 315.
The theory of covering groupoids plays an important role in the applications of groupoids (cf. , ). There are two important results about group-groupoids given in . One is that if X is a topological group whose underlying space has a universal cover, then the category T GCov/X of topological group covers of X is equivalent to the category GpGpdCov/π1X of group-groupoid covers of π1X. The other is that if G is a group-groupoid, then the category the category GpGdCov/G of covering morphisms over G is equivalent to the category GpGdAct(G) of group-groupoid actions of G on groups is equivalent to equivalent. In this paper we introduce the notion of a local group-groupoid as a local group object in the category of gorupoids and prove local group-groupoid version of these results. For the first result we prove that if L is a local topological group, whose underlying topology has a universal cover, then the category LT GCov/L of local topological covers of L and the category LGGdCov/π1(L) of local group-groupoid covers of π1(L) are equivalent. For the second result we prove that if G is a local group-groupoid, then the category LGpGdCov/G of local groupgroupoid covers is equivalent to the category LGpGdAct(G) of local group-groupoid actions of G on local groups.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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