Coverings of Lie groupoids

Authors: İLHAN İÇEN, M. HABİL GÜRSOY, A. FATİH ÖZCAN

Abstract: In this work we constitute the category of coverings of the Lie fundamental groupoid associated with a connected smooth manifold. We show that this category is equivalent to the category of universal coverings of a connected smooth manifold. In addition, we prove the equivalence of the category of coverings of a Lie groupoid and the category of actions of this Lie groupoid on a connected smooth manifold. Also we present two side results related to actions of Lie groupoids on the manifolds and coverings of Lie groupoids.

Keywords: Lie groupoid, covering, action, lifting

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