Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Many-valued complete distributivity   Categories enriched over a commutative unital quantale can be studied as
generalized, or many-valued, ordered structures. Because many concepts, such as
complete distributivity, in lattice theory can be characterized by existence of
certain adjunctions, they can be reformulated in the many-valued setting in
terms of categorical postulations. So, it is possible, by aid of categorical
machineries, to establish theories of many-valued complete lattices,
many-valued completely distributive lattices, and so on. This paper presents a
systematical investigation of many-valued complete distributivity, including
the topics: (1) subalgebras and quotient algebras of many-valued completely
distributive lattices; (2) categories of (left adjoint) functors; and (3) the
relationship between many-valued complete distributivity and properties of the
quantale of truth values. The results show that enriched category theory is a
very useful tool in the study of many-valued versions of order-related
mathematical entities.

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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol