Principal 2-bundles and their gauge 2-groups

Abstract

In this paper we introduce principal 2-bundles and show how they are classified by non-abelian Cech cohomology. Moreover, we show that their gauge 2-groups can be described by 2-group-valued functors, much like in classical bundle theory. Using this, we show that, under some mild requirements, these gauge 2-groups possess a natural smooth structure. In the last section we provide some explicit examples.Comment: 40 pages; v3: completely revised and extended, classification corrected, name changed, to appear in Forum Mat