Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zappa-Sz\'ep products of Garside monoids   A monoid $K$ is the internal Zappa-Sz\'ep product of two submonoids, if every
element of $K$ admits a unique factorisation as the product of one element of
each of the submonoids in a given order. This definition yields actions of the
submonoids on each other, which we show to be structure preserving.
  We prove that $K$ is a Garside monoid if and only if both of the submonoids
are Garside monoids. In this case, these factors are parabolic submonoids of
$K$ and the Garside structure of $K$ can be described in terms of the Garside
structures of the factors. We give explicit isomorphisms between the lattice
structures of $K$ and the product of the lattice structures on the factors that
respect the Garside normal forms. In particular, we obtain explicit natural
bijections between the normal form language of $K$ and the product of the
normal form languages of its factors.

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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex