Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the PROP corresponding to bialgebras   A PROP is a symmetric monoidal category, whose set of objects is the set of
natural numbers and on objects the monoidal structure is given by the addition.
An algebra over a PROP is a symmetric strict monoidal functor to the tensor
category of vector spaces. We give an explicite construction of the PROP whose
category of algebras is equivalent to the category of bialgebras (= associative
and coassociative bialgebras).

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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cs