symmetric monoidal (∞,1)-category of spectra
algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
A sheaf of vertex operator algebras which in degree-0 coincides with the structure sheaf of the base space is a kind of “horizontal categorification” of vertex operator algebra, hence also called a vertex operator algebroid or vertex algebroid for short.
Vassily Gorbounov, Fyodor Malikov, Vadim Schechtman, Gerbes of chiral differential operators. II. Vertex algebroids, Invent. Math. 155 (2004), no. 3, 605–680, MR2005e:17047, math.AG/0003170, doi;
Paul Bressler, Vertex algebroids I (arXiv:math/0202185)
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