Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Existence of Pushouts of Realizability Toposes   We consider two preorder-enriched categories of ordered PCAs:
$\mathsf{OPCA}$, where the arrows are functional morphisms, and $\mathsf{PCA}$,
where the arrows are applicative morphisms. We show that $\mathsf{OPCA}$ has
small products and finite biproducts, and that $\mathsf{PCA}$ has finite
coproducts, all in a suitable 2-categorical sense. On the other hand,
$\mathsf{PCA}$ lacks all nontrivial binary products. We deduce from this that
the pushout, over $\mathsf{Set}$, of two nontrivial realizability toposes is
never a realizability topos.

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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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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: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: cs