Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Brauer diagrams, modular operads, and a graphical nerve theorem for
  circuit algebras   Circuit algebras, used in the study of finite-type knot invariants, are a
symmetric analogue of Jones's planar algebras. They are very closely related to
circuit operads, which are a variation of modular operads admitting an extra
monoidal product. This paper gives a description of circuit algebras in terms
categories of Brauer diagrams. An abstract nerve theorem for circuit operads --
and hence circuit algebras -- is proved using an iterated distributive law, and
an existing nerve theorem for modular operads.

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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph