Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Poincar\'e-Birkhoff-Witt criterion for Koszul operads   The aim of this article is to give a criterion, generalizing the criterion
introduced by Priddy for algebras, to verify that an operad is Koszul. We
define the notion of a Poincare-Birkhoff-Witt basis in the context of operads.
Then we show that an operad having a Poincare-Birkhoff-Witt basis is Koszul.
Besides, we obtain that the Koszul dual operad has also a
Poincare-Birkhoff-Witt basis. We check that the classical examples of Koszul
operads (commutative, associative, Lie) have a Poincare-Birkhoff-Witt basis.

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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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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: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: econ