Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free adequate semigroups   We give an explicit description of the free objects in the quasivariety of
adequate semigroups, as sets of labelled directed trees under a natural
combinatorial multiplication. The morphisms of the free adequate semigroup onto
the free ample semigroup and into the free inverse semigroup are realised by a
combinatorial "folding" operation which transforms our trees into Munn trees.
We use these results to show that free adequate semigroups and monoids are
J-trivial and never finitely generated as semigroups, and that those which are
finitely generated as (2,1,1)-algebras have decidable word problem.

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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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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: dg-ga
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The categories of this paper are: supr-con