Gerbes on Lie groupoids
From CRCG-Wiki
We study (pre-)sheaves in bicategories on geometric categories: smooth manifolds, manifolds with a Lie group action and Lie groupoids. We present three main results: we describe equivariant descent, we generalize the plus-construction to our setting and show that the descent data of a prestack form a stack. Finally we show that, for a stack, the pullback functor along a Morita-equivalence of Lie groupoids is an equivalence of bicategories.
Our results have direct applications to gerbes and 2-vector bundles. We illustrate the usefulness of our results in a systematic discussion of holonomies for unoriented surfaces which have applications in Wess-Zumino terms arising in a Lagrangian description of conformal field theories.
(Joint work with Thomas Nikolaus)
