Local group-groupoids
Küçük Resim Yok
Tarih
2009
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
The theory of covering groupoids plays an important role in the applications of groupoids (cf. [1], [5]). There are two important results about group-groupoids given in [2]. 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/?1X of group-groupoid covers of ?1X. 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/?1(L) of local group-groupoid covers of ?1(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.
Açıklama
Anahtar Kelimeler
Kaynak
International Conference of Mathematical Sciences
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Mucuk, O., Ay, H. Y. ve Bağrıyanık, B. (2009). Local Group-Groupoids. Maltepe Üniversitesi. s. 315.
