Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monads in Double Categories   We extend the basic concepts of Street's formal theory of monads from the
setting of 2-categories to that of double categories. In particular, we
introduce the double category Mnd(C) of monads in a double category C and
define what it means for a double category to admit the construction of free
monads. Our main theorem shows that, under some mild conditions, a double
category that is a framed bicategory admits the construction of free monads if
its horizontal 2-category does. We apply this result to obtain double
adjunctions which extend the adjunction between graphs and categories and the
adjunction between polynomial endofunctors and polynomial monads.

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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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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: physics
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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: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: hep-ph