∞-Lie theory (higher geometry)
(2,1)-quasitopos?
structures in a cohesive (∞,1)-topos
A sheaf of -algebras is a suitable sheaf/stack/∞-stack of L-∞ algebras/dg-Lie algebras.
These structures appear in the deformation theory of the given base space/site: where a single L-∞ algebra is equivalently a formal moduli problem (hence “over the point), so a sheaf of these over some base may be thought of as an -parameterized formal moduli problem (eg. Hinich 03).
Discussion in the context of deformation theory/parameterized formal moduli problems is in
Quasi-coherent sheaves of dg-Lie algebras appear in
Amnon Yekutieli, appendix A of Twisted Deformation Quantization of Algebraic Varieties (arXiv:0905.0488)
I. Ciocan-Fontanine, Mikhail Kapranov, Derived Quot schemes (arXiv:math/9905174)
Discussion in physics, of sheaves of -algebras of physical fields in prequantum field theory includes
Created on January 3, 2014 at 16:24:20. See the history of this page for a list of all contributions to it.