Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Module categories, weak Hopf algebras and modular invariants   We develop abstract nonsense for module categories over monoidal categories
(this is a straightforward categorification of modules over rings). As
applications we show that any semisimple monoidal category with finitely many
simple objects is equivalent to the category of representations of a weak Hopf
algebra (theorem of T. Hayashi) and classify module categories over the fusion
category of $\hat{sl}(2)$ at a positive integer level where we meet once again
ADE classification pattern.

25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph