Simplicial localization of homotopy algebras over a prop

Abstract

We prove that a weak equivalence between two cofibrant (colored) props in chain complexes induces a Dwyer-Kan equivalence between the simplicial localizations of the associated categories of algebras. This homotopy invariance under base change implies that the homotopy category of homotopy algebras over a prop P does not depend on the choice of a cofibrant resolution of P, and gives thus a coherence to the notion of algebra up to homotopy in this setting. The result is established more generally for algebras in combinatorial monoidal dg categories.

slight improvement of the main result, several corrections. Submitted

References in corpus (3)

• Higher Topos Theory
• Operads, homotopy algebra and iterated integrals for double loop spaces
• On homotopy invariance for algebras over colored PROPs