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In this paper we introduce principal 2-bundles and show how they are classified by non-abelian ČČech 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.
Forum Mathematicum – de Gruyter
Published: May 1, 2011
Keywords: Principal bundle; Lie groupoid; categorical Lie group; Morita equivalence
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