symmetric monoidal (∞,1)-category of spectra
Topological chiral homology is a generalization of Hochschild homology. Where Hochschild homology is given by (∞,1)-colimits of functors constant on an -algebra over a diagram that is an ∞-groupoid, topological chiral homology is given by colimits of constant functors over (∞,1)-categories of open subsets of a manifold.
This generalizes the concept of chiral homology by Beilinson-Drinfeld.
The notion of topological chiral homology should be closely related to that of
and be related to concepts in
A quick definition and comments on its relation to FQFT are in section 4.1 of
Technical details are in section 3 of
which meanwhile has becomes part of section 5 of