Up-to-Homotopy Monoids

Abstract

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.

8 pages. Version 2: references added, and phi's changed to xi's

References in corpus (1)

• Homotopy Algebras for Operads

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• Homotopy Algebras for Operads
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• Curved homotopy coalgebras
• Coherence, Homotopy and 2-Theories