nLab
Eilenberg-Zilber operad

Idea

The Eilenberg–Zilber operad ${𝒵}_k$ is the endomorphism operad of the chain complex of chains on the standard $k$-simplex.

By the method of acyclic model?s by Eilenberg and Zilber, one shows that $\mathbb{Z}(\mathrm{\infty })$ is an E-∞ operad (therefore the name).

Applications

• The cochains on simplicial sets are naturally algebras over $𝒵(\mathrm{\infty })$.

References

See the references at cochains on simplicial sets.