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 …

In this paper we introduce a notion of parallel transport for principal bundles with
connections over differentiable stacks. We show that principal bundles with connections …

Atiyah sequences and connections on principal bundles over Lie groupoids and differentiable
stacks Page 1 J. Noncommut. Geom. 17 (2023), 407–437 DOI 10.4171/JNCG/486 © 2023 …

We investigate an interplay between some ideas in traditional gauge theory and certain
concepts in fibered categories. We accomplish this by introducing a notion of a principal Lie …

Let G be a Lie groupoid. The category BG of principal G-bundles defines a differentiable
stack. On the other hand, given a differentiable stack D, there exists a Lie groupoid H such …

Retraction maps on Lie groups can be successfully used in mechanics and control theory to
generate numerical integration schemes, for ordinary differential equations with a variational …

In this PhD thesis, we have studied certain geometric structures over Lie groupoids and
differentiable stacks. This thesis is based on the work [arXiv: 2103.04560, arXiv …

Let 𝕏=[X 1⇉ X 0] be a Lie groupoid equipped with a connection, given by a smooth
distribution ℋ⊂ TX 1 transversal to the fibers of the source map. Under the assumption that …

We introduce the notion of Lusternik-Schnirelmann category for differentiable stacks and
establish its relation with the groupoid Lusternik-Schnirelmann category for Lie groupoids …

Chatterjee, Saikat ; Koushik, Praphulla On two notions of a gerbe over a stack. (English) £ ¢
¡ Zbl 07267887 Bull. Sci. Math Page 1 Chatterjee, Saikat; Koushik, Praphulla On two …