(see also Chern-Weil theory, parameterized homotopy theory)
vector bundle, (∞,1)-vector bundle
topological vector bundle, differentiable vector bundle, algebraic vector bundle
direct sum of vector bundles, tensor product of vector bundles, inner product of vector bundles?, dual vector bundle
group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
For $\mathcal{X}$ an (∞,1)-topos, a 2-gerbe $P$ in $\mathcal{X}$ is an object which is
The first condition says that it is an (∞,1)-sheaf with values in 2-groupoids. The second says that $P \to *$ 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 $P$ is a) locally connected and b) locally non-empty .
For $\mathcal{X}$ an (∞,1)-topos, an abelian 2-gerbe $P$ in $\mathcal{X}$ is an object which is
principal 3-bundle / 2-gerbe / bundle 2-gerbe
A comprehensive discussion of nonabelian 2-gerbes is in
A more expository discussion is in
Abelian 2-gerbes are a special case (see ∞-gerbe) of the discussion in section 7.2.2 of
See also
Last revised on June 29, 2012 at 14:04:01. See the history of this page for a list of all contributions to it.