Classes of bundles
Examples and Applications
Special and general types
For an (∞,1)-topos, a 2-gerbe in is an object which is
The first condition says that it is an (∞,1)-sheaf with values in 2-groupoids. The second says that is an effective epimorphism and that the 0-th homotopy sheaf is the terminal sheaf. In the literature this is often stated as saying that is a) locally connected and b) locally non-empty .
For an (∞,1)-topos, an abelian 2-gerbe in is an object which is
A comprehensive discussion of nonabelian 2-gerbes is in
- Lawrence Breen, On the classification of 2-gerbes and 2-stacks , Astérisque 225 (1994).
A more expository discussion is in
Abelian 2-gerbes are a special case (see ∞-gerbe) of the discussion in section 7.2.2 of
- Ettore Aldrovandi, 2-Gerbes bound by complexes of gr-stacks, and cohomology Journal of Pure and Applied Algebra 212 (2008), 994–103 (pdf)
Revised on June 29, 2012 14:04:01
by Urs Schreiber