Modules over Operads and Functors
By Benoit Fresse. 2007
244 citations recorded by the source corpus.
Categorical and operadic background.- Symmetric monoidal categories for operads.- Symmetric objects and functors.- Operads and algebras in symmetric monoidal categories.- Miscellaneous structures associated to algebras over operads.- The category of right modules over operads and functors.- Definitions and basic constructions.- Tensor products.- Universal constructions on right modules over operads.- Adjunction and embedding properties.- Algebras in right modules over operads.- Miscellaneous examples.- Homotopical background.- Symmetric monoidal model categories for operads.- The homotopy of algebras over operads.- The (co)homology of algebras over operads.- The homotopy of modules over operads and functors.- The model category of right modules.- Modules and homotopy invariance of functors.- Extension and restriction functors and model structures.- Miscellaneous applications.- Appendix: technical verifications.- Shifted modules over operads and functors.- Shifted functors and pushout-products.- Applications of pushout-products of shifted functors.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a95caf9b8694cea2eef74ded50d9291e8a4edf76
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Citations in the corpus
- Curved Koszul duality theory (2010, background): “In the (semi-)model category structure on P-algebras defined in [Fre09], cofibrant P-algebras are retracts of quasi-free P-algebras endowed with a good filtration (Proposition 12.”
- Model structures on commutative monoids in general model categories (2014, background): “Since both O and QCom are Σ-cofibrant, it follows from [15] (Theorem 12.”
- Homological perturbation theory for algebras over operads (2009, background): “I satisfying coassociativity and counit axioms; see Fresse [7, Section 1.2.17], Getzler and Jones [10, Section 1.7] or [28, Section 4.7].”
- Homotopy completion and topological Quillen homology of structured ring spectra (2011, background): “10 to a filtered colimit construction of OB[r] for each r ≥ 0; for other approaches to these types of filtrations compare [22, 70].”
- Homotopy theory of modules over operads in symmetric spectra (2007, background): “3 goes back to Getzler and Jones [10] and Smirnov [40] and more recently appears in Fresse [7; 9], Goerss and Hopkins [12], Kapranov and Manin [22], Kelly [23] and Rezk [35].”