Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A non-commutative Priestley duality   We prove that the category of left-handed strongly distributive skew lattices
with zero and proper homomorphisms is dually equivalent to a category of
sheaves over local Priestley spaces. Our result thus provides a non-commutative
version of classical Priestley duality for distributive lattices and
generalizes the recent development of Stone duality for skew Boolean algebras.
  From the point of view of skew lattices, Leech showed early on that any
strongly distributive skew lattice can be embedded in the skew lattice of
partial functions on some set with the operations being given by restriction
and so-called override. Our duality shows that there is a canonical choice for
this embedding.
  Conversely, from the point of view of sheaves over Boolean spaces, our
results show that skew lattices correspond to Priestley orders on these spaces
and that skew lattice structures are naturally appropriate in any setting
involving sheaves over Priestley spaces.

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The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom