nLab Eilenberg-Zilber operad

Idea

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

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

Applications

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

References

See the references at cochains on simplicial sets.