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Four equivalent versions of nonabelian gerbes

Thomas Nikolaus, Konrad Waldorf
2013 Pacific Journal of Mathematics  
We recall and partially improve four versions of smooth, nonabelian gerbes: Cech cocycles, classifying maps, bundle gerbes, and principal 2-bundles. We prove that all four versions are equivalent, and so establish new relations between interesting recent developments. Prominent partial results that we prove are a bijection between the continuous and smooth nonabelian cohomology, and an explicit equivalence between bundle gerbes and principal 2-bundles as 2-stacks. 6.
doi:10.2140/pjm.2013.264.355 fatcat:jr7mn5qgwnar7g4mr3ei5xh5xq