Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localization of $\frak{u}$-modules. III. Tensor categories arising from
  configuration spaces   This article is a sequel to hep-th/9411050, q-alg/9412017.
  In Chapter 1 we associate with every Cartan matrix of finite type and a
non-zero complex number $\zeta$ an abelian artinian category $\FS$. We call its
objects {\em finite factorizable sheaves}. They are certain infinite
collections of perverse sheaves on configuration spaces, subject to a
compatibility ("factorization") and finiteness conditions.
  In Chapter 2 the tensor structure on $\FS$ is defined using functors of
nearby cycles. It makes $\FS$ a braided tensor category.
  In Chapter 3 we define, using vanishing cycles functors, an exact tensor
functor $$\Phi:\FS\lra\CC$$ to the category $\CC$ connected with the
corresponding quantum group.
  In Chapter 4 we show that $\Phi$ is an equivalence. Some proofs are only
sketched.

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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio