We study (pre-)sheaves in bicategories on geometric categories: smoothmanifolds, manifolds with a Lie group action and Lie groupoids. We presentthree main results: we describe equivariant descent, we generalize the plusconstruction to our setting and show that the plus construction yields a2-stackification for 2-prestacks. Finally we show that, for a 2-stack, thepullback functor along a Morita-equivalence of Lie groupoids is an equivalenceof bicategories. Our results have direct applications to gerbes and 2-vectorbundles. For instance, they allow to construct equivariant gerbes from localdata and can be used to simplify the description of the local data. Weillustrate the usefulness of our results in a systematic discussion ofholonomies for unoriented surfaces.
展开▼
