Four Equivalent Versions of Non-Abelian Gerbes

Understand

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.