Nazmiye ALEMDAR

Topolojik R-Modül Grupoid Örtüleri

Bu makalede ilk olarak bir topolojik R-modül grupoid, topolojik R-modüllerin kategorisinde bir grupoid obje olarak tanımlandı. Daha sonra , birim elemanı olan birimli bir diskre topolojik halka ve topolojik uzayı evrensel örtüye sahip olan bir topolojik -modül olmak üzere temel grupoidinin bir topolojik -modül grupoid olduğu gösterildi. Son olarak da objeleri için N ve birer evrensel örtüye sahip olacak şekilde ModCov/N kategorisinin bir dolu alt kategorisi UModCov/N ve objeleri için de N ve birer evrensel örtüye sahip olacak şekilde GdMCov/ kategorisinin bir dolu alt kategorisi olan GdMCov/ tanımlanıp, ve kategorilerinin denk kategoriler olduğu ispatlanmıştır.

Anahtar Kelimeler:

Grup-grupoid, Örtü grupoidi, R-Modül grupoid, Topolojik R-Modül grupoid

Topological R-Module Groupoid Coverings

In this paper, firstly a topological R-module groupoid is defined as a groupoid object in the category of topological R-modules. Then it is proved that the fundamental groupoid is a topological R-module groupoid, where R is a discrete topological ring with identity 1R and N is a topological R-module whose underlying space has a universal covering. Finally, it is proved that the categories and are equivalent, where UModCov/N is a full subcategory of in which for objects both N and have universal coverings and GdMCov/ is the full subcategory of GdMCov/ in which for objects both and N have universal coverings.

Keywords:

Group-groupoid, Covering groupoid, R-Module groupoid, Topological R-Module groupoid,

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