Title: A GNS construction of three-dimensional abelian Dijkgraaf-Witten theories,
Abstract: We give a detailed account of the so-called "universal construction" that
aims to extend invariants of closed manifolds, possibly with additional
structure, to topological field theories and show that it amounts to a
generalization of the GNS construction. We apply this construction to an
invariant defined in terms of the groupoid cardinality of groupoids of bundles
to recover Dijkgraaf-Witten theories, including the vector spaces obtained as a
linearization of spaces of principal bundles.