Atiyah sequence and gauge transformations of a principal 2-bundle over a Lie groupoid

Abstract

In this paper, we introduce a notion of a principal 2-bundle over a Lie groupoid. For such principal 2-bundles, we have produced a short exact sequence of VB-groupoids, namely, the Atiyah sequence. Two notions of connection structures viz. strict connections and semi-strict connections on a principal 2-bundle arising respectively, from a retraction of the Atiyah sequence and a retraction up to a natural isomorphism have been introduced. We have constructed a class of principal -bundles and connections from a given principal -bundle over with connection. An existence criterion for the connections on a principal 2-bundle over a proper, étale Lie groupoid is proposed. We have studied the action of the 2-group of gauge transformations on the category of strict and semi-strict connections. Finally, we have observed an extended symmetry of the category of semi-strict connections.