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.
Lie groupoid, covering, action, lifting
İÇEN, İLHAN; GÜRSOY, M. HABİL; and ÖZCAN, A. FATİH
"Coverings of Lie groupoids,"
Turkish Journal of Mathematics: Vol. 35:
2, Article 4.
Available at: https://journals.tubitak.gov.tr/math/vol35/iss2/4