1999/12/10 by Tom Leinster, Leinster, Tom
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.AT #math.CT #math.QA
paper · pdf · doi:10.48550/arxiv.math/9912084
8 pages. Version 2: references added, and phi's changed to xi's
openalex publication_date 1999/12/10 · arxiv created 2000/02/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.