Springer Iranian Journal of Science 2731-8095 37 1 2013 03 01 Geometrical Categories of Generalized Lie Groups and Lie Group-Groupoids 69 73 1539 10.22099/ijsts.2013.1539 EN M. R. Farhangdoost Department of Mathematics, College of Sciences, Shiraz University, P.O. Box 71457- 44776, Shiraz, Iran T. Nasirzade Department of Mathematics, College of Sciences, Shiraz University, P.O. Box 71457- 44776, Shiraz, Iran Journal Article 2012 05 08 In this paper we construct the category of coverings of fundamental generalized Lie group-groupoid associated<br />with a connected generalized Lie group. We show that this category is equivalent to the category of coverings of a<br />connected generalized Lie group. In addition, we prove the category of coverings of generalized Lie groupgroupoid<br />and the category of actions of this generalized Lie group-groupoid on a connected generalized Lie group<br />are equivalent. Lie groupoid Lie group Generalized Lie group Homotopy of topological groups https://ijsts.shirazu.ac.ir/article_1539_d2b3b087ae633e4d8582ad88e3e085ed.pdf