A d-dimensional extended TQFT is a symmetric monoidal 2-functor out of a symmetric monoidal bicategory (SMB) of d-bordisms. Following Freed-Hopkins-Lurie-Teleman, I will describe a framework for constructing the partition function Z of the Dijkgraaf-Witten (DW TQFT) theory that factors through an SMB of bispans. 

A key result I will discuss is the characterisation of a 2-functor out of a bicategory of bispans. An example of such a 2-functor will be discussed. A DW TQFT can be constructed if a stronger statement involving a symmetric monoidal structure is found.

A finite 2-group X is a connected 2-type with finite homotopy groups.  I will explicitly describe the path groupoid of the derived mapping space of maps from a 2-sphere to X. Assuming the DW TQFT exists, I will explain the relation between mapping spaces and the TQFT. The value of a 3-dimensional theory Z on a 2-sphere will follow