Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group categories and their field theories   A group-category is an additively semisimple category with a monoidal product
structure in which the simple objects are invertible. For example in the
category of representations of a group, 1-dimensional representations are the
invertible simple objects. This paper gives a detailed exploration of
"topological quantum field theories" for group-categories, in hopes of finding
clues to a better understanding of the general situation. Group-categories are
classified in several ways extending results of Froelich and Kerler.
Topological field theories based on homology and cohomology are constructed,
and these are shown to include theories obtained from group-categories by
Reshetikhin-Turaev constructions. Braided-commutative categories most naturally
give theories on 4-manifold thickenings of 2-complexes; the usual 3-manifold
theories are obtained from these by normalizing them (using results of Kirby)
to depend mostly on the boundary of the thickening. This is worked out for
group-categories, and in particular we determine when the normalization is
possible and when it is not.

34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg