FQFT and cohomology
Types of quantum field thories
For a symmetric monoidal (infinity,2)-category, a Calabi-Yau object in is
This is (Lurie, def. 4.2.6).
Then a Calabi-Yau object in is an algebra object equipped with an -equivariant morphism
satisfying the condition that the composite morphism
exhibits as its own dual .
Such an algebra object is called a Calabi-Yau algebra object.
This is (Lurie, example 4.2.8).
A version of the cobordism hypothesis says that symmetric monoidal -functors
out of a version of the (infinity,2)-category of cobordisms where all 2-cobordisms have at least one outgoing (ingoing) boundary component, are equivalently given by their value on the point, which is a Calabi-Yau object in .
This is Lurie, 4.2.11.
Section 4.2 of