$A_\infty$-monads and completion

Tilman Bauer and Assaf Libman

Given an operad $A$ of topological spaces, we consider $A$-monads in a topological category $\C$. When $A$ is an $A_\infty$-operad, any $A$-monad $K \colon \C \to \C$ can be thought of as a monad up to coherent homotopies. We define the completion functor with respect to an $A_\infty$-monad and prove that it is an $A_\infty$-monad itself.

Journal of Homotopy and Related Structures, Vol. 5(2010), No. 1, pp. 133-155