A-infinity monads and completion

Mathematics – Algebraic Topology

Scientific paper

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23 pages. Minor errors corrected. This version will appear in the Journal of Homotopy and Related Structures

Scientific paper

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

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