Скачать или смотреть Emily Cliff : Smooth 2-groups and their principal bundles

A 2-group is a categorical generalization of a group: it's a category with a multiplication operation which satisfies the usual group axioms only up to coherent isomorphisms. In this talk I will introduce the category of Lie groupoids and bibundles between them, in order to provide the definition of a smooth 2-group. I will define principal bundles for such a smooth 2-group, and provide classification results that allow us to compare them to principal bundles for ordinary groups. As a consequence in specific settings, we obtain a categorification of the Freed--Quinn line bundle over the moduli stack Bun_G(X) for a finite group G and Riemann surface X. This is a line bundle which plays an important role in Dijkgraaf--Witten theory (i.e. Chern--Simons theory for the finite group G). This talk is based on joint work with Dan Berwick-Evans, Laura Murray, Apurva Nakade, and Emma Phillips. I will not assume any previous background on 2-groups, Lie groupoids, or Dijkgraaf--Witten theory.