Four Equivalent Versions of Non-Abelian Gerbes

Abstract

We recall and partially improve four versions of smooth, non-abelian gerbes: Cech cocycles, classifying maps, bundle gerbes, and principal 2-bundles. We prove that all these four versions are equivalent, and so establish new relations between interesting recent developments. Prominent partial results we prove are a bijection between continuous and smooth non-abelian cohomology, and an explicit equivalence between bundle gerbes and principal 2-bundles as 2-stacks.

65 pages, v2: minor corrections, new Corollary 7.2 about equivariant gerbes; v3: again minor corrections; v3 is the final and published version

References in corpus (4)

• Topological and Smooth Stacks
• Higher gauge theory I: 2-Bundles
• Butterflies I: morphisms of 2-group stacks
• More Morphisms between Bundle Gerbes

Cited by in corpus (7)

• Čech cocycles for differential characteristic classes -- An infinity-Lie theoretic construction
• Non-Abelian Tensor Multiplet Equations from Twistor Space
• A Construction of String 2-Group Models using a Transgression-Regression Technique
• Non-abelian higher gauge theory and categorical bundle
• Integrating central extensions of Lie algebras via Lie 2-groups
• Higher Structures: gerbes and Nijenhuis forms
• Lie groupoids and crossed module-valued gerbes over stacks