Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the 2-categories of weak distributive laws   A weak mixed distributive law (also called weak entwining structure) in a
2-category consists of a monad and a comonad, together with a 2-cell relating
them in a way which generalizes a mixed distributive law due to Beck. We show
that a weak mixed distributive law can be described as a compatible pair of a
monad and a comonad, in 2-categories extending, respectively, the 2-category of
comonads and the 2-category of monads. Based on this observation, we define a
2-category whose 0-cells are weak mixed distributive laws. In a 2-category K
which admits Eilenberg-Moore constructions both for monads and comonads, and in
which idempotent 2-cells split, we construct a fully faithful 2-functor from
this 2-category of weak mixed distributive laws to K^{2 x 2}.

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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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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: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas