Geometrical Categories of Generalized Lie Groups and Lie Group-Groupoids

Abstract

In this paper we construct the category of coverings of fundamental generalized Lie group-groupoid associatedwith a connected generalized Lie group. We show that this category is equivalent to the category of coverings of aconnected generalized Lie group. In addition, we prove the category of coverings of generalized Lie groupgroupoidand the category of actions of this generalized Lie group-groupoid on a connected generalized Lie groupare equivalent.