Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomology of idempotent braidings, with applications to factorizable
  monoids   We develop new methods for computing the Hochschild (co)homology of monoids
which can be presented as the structure monoids of idempotent set-theoretic
solutions to the Yang--Baxter equation. These include free and symmetric
monoids; factorizable monoids, for which we find a generalization of the
K{\"u}nneth formula for direct products; and plactic monoids. Our key result is
an identification of the (co)homologies in question with those of the
underlying YBE solutions, via the explicit quantum symmetrizer map. This
partially answers questions of Farinati--Garc{\'i}a-Galofre and Dilian Yang. We
also obtain new structural results on the (co)homology of general YBE
solutions.

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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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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: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-th