Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fixed points of endomorphisms and relations between metrics in
  preGarside monoids   Rodaro and Silva proved that the fixed points submonoid and the periodic
points submonoid of a trace monoid endomorphism are always finitely generated.
We show that for finitely generated left preGarside monoids, that includs
finitely generated preGarside monoids, Garside monoids and Artin monoids, the
fixed and periodic points submonoids of any endomorphism are also finitely
generated left preGarside monoids under some condition, and in the case of
Artin monoids, these submonoids are always Artin monoids too. We also prove
algebraically some inequalities, equivalences and non-equivalences between
three metrics in finitely generated preGarside monoids, and especially in trace
monoids and Garside monoids.

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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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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: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol