Classical and quantum Chern-Simons with gauge group U(1)N were
classified by Belov and Moore in \cite{belov_moore}. They studied both ordinary
topological quantum field theories as well as spin theories. On the other hand
a correspondence is well known between ordinary (2+1)-dimensional TQFTs and
modular tensor categories. We study group categories and extend them slightly
to produce modular tensor categories that correspond to toral Chern-Simons.
Group categories have been widely studied in other contexts in the literature
\cite{frolich_kerler},\cite{quinn},\cite{joyal_street},\cite{eno},\cite{dgno}.
The main result is a proof that the associated projective representation of the
mapping class group is isomorphic to the one from toral Chern-Simons. We also
remark on an algebraic theorem of Nikulin that is used in this paper.Comment: 152 page
