Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact factorizations and extensions of fusion categories   We introduce and study the new notion of an {\em exact factorization}
$\mathcal{B}=\mathcal{A}\bullet \mathcal{C}$ of a fusion category $\mathcal{B}$
into a product of two fusion subcategories $\mathcal{A},\mathcal{C}\subseteq
\mathcal{B}$ of $\mathcal{B}$. This is a categorical generalization of the well
known notion of an exact factorization of a finite group into a product of two
subgroups. We then relate exact factorizations of fusion categories to exact
sequences of fusion categories with respect to an indecomposable module
category, which was introduced and studied by P. Etingof and the author in
\cite{EG}. We also apply our results to study extensions of a group-theoretical
fusion category by another one, provide some examples, and propose a few
natural questions.

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The categories of this paper are: nlin
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: q-bio