Homotopy theory of modules over operads and non-\(\varSigma \) operads in monoidal model categories

DOI10.1016/j.jpaa.2009.11.006zbMath1231.55011arXiv0801.0191OpenAlexW2047194786MaRDI QIDQ2268571

John E. Harper

Publication date: 8 March 2010

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.0191

zbMATH Keywords

operadmodel category

Mathematics Subject Classification ID

Abstract and axiomatic homotopy theory in algebraic topology (55U35) Spectra with additional structure ((E_infty), (A_infty), ring spectra, etc.) (55P43) Loop space machines and operads in algebraic topology (55P48)

Related Items

Higher homotopy excision and Blakers-Massey theorems for structured ring spectra ⋮ \(\mathsf{TQ}\)-completion and the Taylor tower of the identity functor ⋮ Preorientations of the derived motivic multiplicative group ⋮ Correction to: ``Homotopy theory of nonsymmetric operads. I--II ⋮ Projective and Reedy model category structures for (infinitesimal) bimodules over an operad ⋮ Derived \(A_\infty\)-algebras in an operadic context ⋮ Derived homotopy algebras ⋮ A model structure on categories related to the categories of complexes ⋮ Homotopy completion and topological Quillen homology of structured ring spectra ⋮ Bousfield localization and algebras over colored operads ⋮ Homotopy theory of nonsymmetric operads ⋮ Model structures on commutative monoids in general model categories ⋮ Homotopy theory of modules over operads in symmetric spectra ⋮ Cohomology of generalized configuration spaces ⋮ A nilpotent Whitehead theorem for \(\mathsf{TQ} \)-homology of structured ring spectra ⋮ On the Maurer-Cartan simplicial set of a complete curved \(A_{\infty}\)-algebra ⋮ Homotopical adjoint lifting theorem ⋮ SYMMETRIC OPERADS IN ABSTRACT SYMMETRIC SPECTRA ⋮ Bar constructions and Quillen homology of modules over operads ⋮ The folk model category structure on strict $\omega$-categories is monoidal

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homotopy theory of modules over operads in symmetric spectra
• Modules in monoidal model categories
• Lie theory of formal groups over an operad.
• Koszul duality for operads
• Homotopy coherent category theory and \(A_\infty\)-structures in monoidal categories
• Axiomatic homotopy theory for operads
• \(E_{\infty}\) algebras and \(p\)-adic homotopy theory
• Homology and cohomology of \(E_\infty\) ring spectra
• Rings, modules, and algebras in infinite loop space theory
• Modules over operads and functors
• Homotopical algebra
• Rational homotopy theory
• The geometry of iterated loop spaces
• Modules and Morita theorem for operads
• Homotopy theory of diagrams
• Homological algebra of homotopy algebras
• Algebras and Modules in Monoidal Model Categories
• Symmetric spectra
• The units of a ring spectrum and a logarithmic cohomology operation
• Simplicial homotopy theory
• Homology
• Homotopy theoretic methods in group cohomology
• Spectra and symmetric spectra in general model categories