  In this paper, we describe a relation between a categorical quantization
construction, called "2-linearization", and extended topological quantum field
theory (ETQFT). We then describe an extension of the 2-linearization process
which incorporates cohomological twisting. The 2-linearization process assigns
2-vector spaces to (finite) groupoids, functors between them to spans of
groupoids, and natural transformations to spans between these. By applying this
to groupoids which represent the (discrete) moduli spaces for topological gauge
theory with finite group G, the ETQFT obtained is the untwisted
Dijkgraaf-Witten (DW) model associated to G. This illustrates the factorization
of TQFT into "classical field theory" valued in groupoids, and "quantization
functors", which has been described by Freed, Hopkins, Lurie and Teleman. We
then describe how to extend this to the full DW model, by using a
generalization of the symmetric monoidal bicategory of groupoids and spans
which incorporates cocycles. We give a generalization of the 2-linearization
functor which acts on groupoids and spans which have associated cohomological
data. We show how the 3-cocycle {\omega} on the classifying space BG which
appears in the action for the DW model induces a classical field theory valued
in this bicategory.
