5
$\begingroup$

In Lurie's On the Classification of Topological Field Theories, one of the main characters are $(\infty,n)$-symmetric monoidal category with duals. A basic example of this should be $n$-vector spaces, and so it is natural to extend this intuition to $n$-modules on a commutative ring, which in nice cases should be the local picture of $n$-vector bundles on a topological space, and in the general situation of quasi-coherent sheaves of $n$-modules over a ringed space.

Is there any available treatment of this subject?

Thanks,

d.

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ I don't even know any references for $n$-vector spaces, $n$-modules, $n$-algebras, etc. $\endgroup$
    – Kevin H. Lin
    Commented Nov 26, 2010 at 6:31
  • $\begingroup$ One of the possible meanings (maybe not the most standard) of "n-vector space" is complex of vector spaces that is concentrated in degrees {0,1,..,n-1}. $\endgroup$
    – André Henriques
    Commented Nov 26, 2010 at 8:27
  • 1
    $\begingroup$ Toen and Vezzosi have some thoughts about $n=2$. Also, they give further references. arXiv:0804.1274, arXiv:0903.3292. $\endgroup$
    – Chris Brav
    Commented Nov 26, 2010 at 9:16

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .