FQFT and cohomology
In the case that is a category of positive energy representations of a loop group of a Lie group , then this algebraically defined QFT is thought to be the result of quantization of Chern-Simons theory over the group .
See at quantization of Chern-Simons theory for more on this.
A standard textbook account is
(See the dedicated page Help me! I'm trying to understand Bakalov and Kirillov for help with understanding the computations in this book.)
and references cited there.