Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Borel Functors and Infinitary Interpretations   We introduce the notion of infinitary interpretation of structures. In
general, an interpretation between structures induces a continuous homomorphism
between their automorphism groups, and furthermore, it induces a functor
between the categories of copies of each structure. We show that for the case
of infinitary interpretation the reversals are also true: Every
Baire-measurable homomorphism between the automorphism groups of two countable
structures is induced by an infinitary interpretation, and every
Baire-measurable functor between the set of copies of two countable structures
is induced by an infinitary interpretation. Furthermore, we show the
complexities are maintained in the sense that if the functor is
$\mathbf{\Delta}^0_\alpha$, then the interpretation that induces it is
$\Delta^{\mathtt{in}}_\alpha$ up to $\mathbf{\Delta}^0_\alpha$ equivalence.

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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn