Categorification of Dijkgraaf-Witten Theory

The goal of my talk is to categorify Dijkgraaf-Witten theory, i.e., gauge theory
with a finite gauge group, aiming at providing foundation for a direct construction
of Dijkgraaf-Witten theory as an Extended Topological Quantum Field Theory.
The main tool is cohomology with coefficients in a Picard groupoid, namely the
Picard groupoid of hermitian lines. I will define cap product between homology
and cohomology with coefficients in Picard groupoids and use it to construct
Dijkgraaf-Witten theory in arbitrary dimension as a functor from the category of
cobordisms to that of vector spaces. This is a joint work with my graduate student
Amit Sharma.