E-infinity operad

Summary

An $E_\infty$ operad is a topological operad whose spaces of $n$-ary operations are contractible and carry a free action of the symmetric group $\Sigma_n$. An algebra over it is a space or spectrum with a multiplication that is commutative and associative up to a coherent system of homotopies. Such algebras model infinite loop spaces and $E_\infty$ ring spectra, the homotopy-theoretic version of commutative rings.