group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
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 $\infty$-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.
For the moment see the section Topological chiral homology at the entry on Hochschild homology.
The notion of topological chiral homology should be closely related to that of
and be related to concepts in
Other related concepts
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