Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A countable family of finitely presented infinite congruence-free
  monoids   We prove that monoids $\mathrm{Mon}\langle a,b,c,d : a^nb=0, ac=1, db=1,
dc=1, dab=1, da^2b=1, \ldots, da^{n-1}b=1\rangle$ are congruence-free for all
$n\geq 1$. This provides a new countable family of finitely presented
congruence-free monoids, bringing one step closer to understanding the
Boone--Higman Conjecture. We also provide examples which show that finitely
presented congruence-free monoids may have quadratic Dehn function.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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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: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat