Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wreaths, mixed wreaths and twisted coactions   Distributive laws between two monads in a 2-category $\CK$, as defined by Jon
Beck in the case $\CK=\mathrm{Cat}$, were pointed out by the author to be
monads in a 2-category $\mathrm{Mnd}\CK$ of monads. Steve Lack and the author
defined wreaths to be monads in a 2-category $\mathrm{EM}\CK$ of monads with
different 2-cells from $\mathrm{Mnd}\CK$.
  Mixed distributive laws were also considered by Jon Beck, Mike Barr and,
later, various others, they are comonads in $\mathrm{Mnd}\CK$. Actually, as
pointed out by John Power and Hiroshi Watanabe, there are a number of dual
possibilities for mixed distributive laws.
  It is natural then to consider mixed wreaths as we do in this article, they
are comonads in $\mathrm{EM}\CK$. There are also mixed opwreaths: comonoids in
the Kleisli construction completion $\mathrm{Kl}\CK$ of $\CK$. The main example
studied here arises from a twisted coaction of a bimonoid on a monoid.
Corresponding to the wreath product on the mixed side is wreath convolution,
which is composition in a Kleisli-like construction. Walter Moreira's
Heisenberg product of linear endomorphisms on a Hopf algebra, is an example of
such convolution, actually involving merely a mixed distributive law.
Monoidality of the Kleisli-like construction is also discussed.

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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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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: eess
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: q-bio