Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Introducing sheaves over commutative semicartesian quantales   We extend the classic definition of sheaves on locales introducing an
original notion of sheaves on semicartesian quantales. We show that the
resulting category and the category of sheaves on locales share similar
categorical properties, and discuss the difficulties in concluding whether our
sheaves on quantales form a Grothendieck topos. We also prove a base change
theorem, which may be useful not only to study the relation between sheaves on
locales and sheaves on quantales, but also may be applied in the presence of an
isomorphism of commutative and unital rings.

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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph