The Boardman-Vogt Resolution of Operads in Monoidal Model Categories

Abstract

We extend the W-construction of Boardman and Vogt to operads of an arbitrary monoidal model category with suitable interval, and show that it provides a cofibrant resolution for well-pointed -cofibrant operads. The standard simplicial resolution of Godement as well as the cobar-bar chain res- olution are shown to be particular instances of this generalisedW-construction.