Cofibrant operads and universal E-infinity operads

Abstract

We introduce various homotopy structures on the category of operads, which shed some light into the homotopy theoretic nature of the barconstruction WB of an operad, the whiskering process for operads and the Sigma-freeness condition. Using the lifting property of cofibrant objects, we construct E-infinity operads A which are universal: any E-infinity-structure lifts to an A-structure, canonically up to homotopy through A-structures. (C) 2003 Elsevier B.V. All rights reserved.