A model structure for coloured operads in symmetric spectra

Abstract

We describe a model structure for coloured operads with values in the category of symmetric spectra (with the positive model structure), in which fibrations and weak equivalences are defined at the level of the underlying collections. This allows us to treat R-module spectra (where R is a cofibrant ring spectrum) as algebras over a cofibrant spectrum-valued operad with R as its first term. Using this model structure, we give suficient conditions for homotopical localizations in the category of symmetric spectra to preserve module structures.

16 pages

References in corpus (3)

• Rings, modules, and algebras in infinite loop space theory
• The Boardman-Vogt resolution of operads in monoidal model categories
• Localization of algebras over coloured operads

Cited by in corpus (9)

• Model Structures on Commutative Monoids in General Model Categories
• Admissibility and rectification of colored symmetric operads
• Genuine equivariant operads
• A Model Structure for Enriched Coloured Operads
• Comparing localizations across adjunctions
• Homotopy theory of equivariant operads with fixed colors
• Quillen cohomology of enriched operads
• Transfer of algebras over operads along derived Quillen adjunctions
• Hochschild and cotangent complexes of operadic algebras