On homotopy invariance for algebras over colored PROPs

Abstract

Over a monoidal model category, under some mild assumptions, we equip the categories of colored PROPs and their algebras with projective model category structures. A Boardman-Vogt style homotopy invariance result about algebras over cofibrant colored PROPs is proved. As an example, we define homotopy topological conformal field theories and observe that such structures are homotopy invariant.

final version, to appear in Journal of Homotopy and Related Structures

References in corpus (5)

• Algebras and modules in monoidal model categories
• Batalin-Vilkovisky algebras and two-dimensional topological field theories
• Notes on string topology
• Homotopy Diagrams of Algebras
• Localization of algebras over coloured operads

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• The homotopy theory of simplicial props
• Smith Ideals of Operadic Algebras in Monoidal Model Categories
• Hom-algebras via PROPs
• On rectification and enrichment of infinity properads
• The Dwyer-Kan model structure for enriched coloured PROPs
• Dwyer-Kan Homotopy Theory of Algebras over Operadic Collections
• Quillen cohomology of enriched operads
• Simplicial localization of homotopy algebras over a prop
• On modified Reedy and modified projective model structures
• Transfer of algebras over operads along derived Quillen adjunctions
• Categorifying equivariant monoids
• Shifted double Lie-Rinehart algebras
• Formality of $A_{\infty }$-Algebras