Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A reference for categorical structures on $\mathbf{Poly}$   In this document, we collect a list of categorical structures on the category
$\mathbf{Poly}$ of polynomial functors. There is no implied claim that this
list is in any way complete. It includes: eight monoidal structures, seven of
which are symmetric, two of which are closed, several of which distribute,
several of which interact duoidally; it also includes a right-coclosure and two
indexed left coclosures; it also includes various adjunctions of which
$\mathbf{Poly}$ is a part, including the free monad and cofree comonad and
their interaction with various monoidal structures.

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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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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: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin