  We prove a decomposition formula for the dimensional reduction of an extended
topological field theory that arises as an orbifold of an equivariant
topological field theory. Our decomposition formula can be expressed in terms
of a categorification of the integral with respect to groupoid cardinality. The
application of our result to topological field theories of Dijkgraaf-Witten
type proves a recent conjecture of Qiu-Wang.
