(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
A 2-module bundle / 2-vector bundle is a fiber ∞-bundle whose typical fiber is a 2-module/2-vector space.
Let $R$ be a commutative ring, or more generally an E-∞ ring. By the discussion at 2-vector space consider the 2-category
equivalent to that whose objects are associative algebras (or generally algebras) $A$ over $R$, (being placeholders for the 2-vector space $A Mod$ which is the category of modules over $A$) whose 1-morphisms are bimodules between these algebras (inducing linear functors between the corresponding 2-vector spaces = categories of modules) and whose 2-morphisms are homomorphisms between those.
Under Isbell duality and by the discussion at Modules – as generalized vector bundles we may think of this 2-category as being that of (generalized) 2-vector bundles over a space called $Spec R$.
Last revised on February 5, 2013 at 02:34:05. See the history of this page for a list of all contributions to it.