Parallel transport on a Lie 2-group bundle over a Lie groupoid along Haefliger paths

Autor:	Chatterjee, Saikat, Chaudhuri, Adittya
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry Mathematical Physics Mathematics - Category Theory Primary 53C08 Secondary 22A22 58H05
Druh dokumentu:	Working Paper
Popis:	We prove a Lie 2-group torsor version of the well-known one-one correspondence between fibered categories and pseudofunctors. Consequently, we obtain a weak version of the principal Lie group bundle over a Lie groupoid. The correspondence also enables us to extend a particular class of principal 2-bundles to be defined over differentiable stacks. We show that the differential geometric connection structures introduced in the authors' previous work, combine nicely with the underlying fibration structure of a principal 2-bundle over a Lie groupoid. This interrelation allows us to derive a notion of parallel transport in the framework of principal 2-bundles over Lie groupoids along a particular class of Haefliger paths. The corresponding parallel transport functor is shown to be smooth. We apply our results to examine the parallel transport on an associated VB-groupoid.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.05355 Zobrazit plný text záznamu View this record from Arxiv