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