Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Up-to-Homotopy Monoids   Informally, a homotopy monoid is a monoid-like structure in which properties
such as associativity only hold `up to homotopy' in some consistent way. This
short paper comprises a rigorous definition of homotopy monoid and a brief
analysis of some examples. It is a much-abbreviated version of the paper
`Homotopy Algebras for Operads' (math.QA/0002180), and does not assume any
knowledge of operads.

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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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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: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci