Algebras and modules in monoidal model categories

Abstract

We construct model category structures for monoids and modules in symmetric monoidal model categories which satisfy an extra axiom, the monoidal axiom, with applications to symmetric spectra and $\Gamma$-spaces.

Cited by in corpus (239)

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• Equivalences of monoidal model categories
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• Global homotopy theory
• From algebraic cobordism to motivic cohomology
• Nilpotence and descent in equivariant stable homotopy theory
• Motivic cell structures
• Diagram spaces and symmetric spectra
• Shifted Poisson Structures and Deformation Quantization
• Simplicial structures on model categories and functors
• Model Structures on Commutative Monoids in General Model Categories
• Operads, Algebras and Modules in General Model Categories
• Derived Algebraic Geometry III: Commutative Algebra
• A necessary and sufficient condition for induced model structures
• Homotopy theory for algebras over polynomial monads
• Homotopy limits and colimits and enriched homotopy theory
• Derived Algebraic Geometry V: Structured Spaces
• The Boardman-Vogt resolution of operads in monoidal model categories
• Topological Hochschild homology of Thom spectra and the free loop space
• Admissibility and rectification of colored symmetric operads
• An algebraic model for commutative HZ-algebras
• On the homotopy theory of enriched categories
• Encoding Equivariant Commutativity via Operads
• Models of G-spectra as presheaves of spectra
• Mixed Weil cohomologies
• Presentably symmetric monoidal infinity-categories are represented by symmetric monoidal model categories
• Topological K-theory of complex noncommutative spaces
• Local duality in algebra and topology
• Rectification of enriched infinity-categories
• Genuine equivariant operads
• Enhancing the filtered derived category
• Homotopy theory of modules over operads in symmetric spectra
• On homotopy invariance for algebras over colored PROPs
• Pro-algebraic homotopy types
• A general framework for homotopic descent and codescent
• Morita theory in abelian, derived and stable model categories
• On Davis-Januszkiewicz homotopy types I; formality and rationalisation
• Homotopy theory of non-symmetric operads
• Diagram spaces, diagram spectra, and spectra of units
• Equivariant homotopy theory for pro-spectra
• Stable Infinity Categories
• Derived coisotropic structures I: affine case
• A curious example of two model categories and some associated differential graded algebras
• (Infinity,2)-Categories and the Goodwillie Calculus I
• Homotopical Quantum Field Theory
• Fixed point theory and trace for bicategories
• Bar constructions and Quillen homology of modules over operads
• Topological Hochschild and cyclic homology for Differential graded categories
• Modules in Monoidal Model Categories
• Smashing localizations of rings of weak global dimension at most one
• Infinity Operads and Monoidal Categories with Group Equivariance
• Schematic homotopy types and non-abelian Hodge theory
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• Homotopy completion and topological Quillen homology of structured ring spectra
• String topology and the based loop space
• Equivariant Structure on Smash Powers
• A motivic version of the theorem of Fontaine and Wintenberger
• DG-algebras and derived A-infinity algebras
• An algebraic model for rational torus-equivariant spectra
• Group completion and units in I-spaces
• Commutative ring objects in pro-categories and generalized Moore spectra
• Abstract representation theory of Dynkin quivers of type A
• Multiplicative structures on homotopy spectral sequences II
• Localization of algebras over coloured operads
• Two results from Morita theory of stable model categories
• Brauer groups and Galois cohomology of commutative ring spectra
• Enriched model categories and presheaf categories
• A Model Structure for Enriched Coloured Operads
• Homotopy units in A-infinity algebras
• Noncommutative Motives I: A Universal Characterization of the Motivic Stable Homotopy Theory of Schemes
• A general context for Goodwillie Calculus
• Postnikov extensions of ring spectra
• Witt sheaves and the $\eta$-inverted sphere spectrum
• On the Algebraic Classification of Module Spectra
• Symmetric spectra model global homotopy theory of finite groups
• The Homotopy Theory of Simplicially Enriched Multicategories
• Derived Algebraic Geometry IV: Deformation Theory
• Homological Algebra for Superalgebras of Differentiable Functions
• Cofibrancy of operadic constructions in positive symmetric spectra
• Derived Algebraic Geometry VI: E_k Algebras
• Dalian notes on rational Pontryagin classes
• Reconstructing rational stable motivic homotopy theory
• A May-type spectral sequence for higher topological Hochschild homology
• Homotopical Algebraic Context over Differential Operators
• Algebraic Geometry over model categories (a general approach to derived algebraic geometry)
• The Left Localization Principle, completions, and cofree $G$-spectra
• Proper equivariant stable homotopy theory
• On exotic equivalences and a theorem of Franke
• The 0-th stable A^1-homotopy sheaf and quadratic zero cycles
• Rational Equivariant Spectra
• Algebras of higher operads as enriched categories II
• Classification of stable model categories
• Dwyer-Kan homotopy theory of enriched categories
• Symmetric operads in abstract symmetric spectra
• Equivariant Topology of Configuration Spaces
• HZ-algebra spectra are differential graded algebras
• Right Bousfield Localization and Operadic Algebras
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• On algebraic structures of the Hochschild complex
• Hodge filtered complex bordism
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• T-model structures on chain complexes of presheaves
• Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces
• Relative left properness of colored operads
• The factorization theory of Thom spectra and twisted non-abelian Poincaré duality
• Equivariant motivic homotopy theory
• Corrections to "Homotopy theory of nonsymmetric operads, I, II"
• On the unit of a monoidal model category
• Homotopy theory of non-symmetric operads II: change of base category and left properness
• Moduli spaces of algebras over non-symmetric operads
• Azumaya Objects in Triangulated Bicategories
• Moduli of objects in dg-categories
• Equivariant stable categories for incomplete systems of transfers
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• Homotopy theory of Spectral categories
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• Motivic twisted K-theory
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• An alternative approach to equivariant stable homotopy theory
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• The Action of Young Subgroups on the Partition Complex
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• A functorial approach to rank functions on triangulated categories
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• Enhanced finite triangulated categories
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• Enhanced $A$-infinity obstruction theory
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• Algebraic models of change of groups functors in (co)free rational equivariant spectra
• Correction to: HZ-algebra spectra are differential graded algebras
• From fibered symmetric bimonoidal categories to symmetric spectra
• The Eilenberg-Watts theorem in homotopical algebra
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• On topological Hochschild homology of the $K(1)$-local sphere
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• Deformation theory of perfect complexes and traces
• Comparing localizations across adjunctions
• Operads in Unstable Global Homotopy Theory
• Homotopy theory of net representations
• Atiyah-Segal Derived Completions for Equivariant Algebraic G-Theory and K-Theory
• The model structure for chain complexes
• Dwyer-Kan Homotopy Theory of Algebras over Operadic Collections
• The Dwyer-Kan model structure for enriched coloured PROPs
• Homotopy theory in a quasi-abelian category
• Operads, modules and topological field theories
• Formal loops, Tate objects and tangent Lie algebras
• Flatness and Shipley's algebraicization theorem
• The Dold-Kan Correspondence and Coalgebra Structures
• Motivic and Étale Spanier-Whitehead duality and the Becker-Gottlieb transfer
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• Symmetric ring spectra and topological Hochschild homology
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• Bousfield localisations along Quillen bifunctors
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• On the homotopy theory of spectral categories
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• K-theoretic descent and a motivic Atiyah-Segal theorem
• Levels of algebraicity in stable homotopy theories
• Galois descent for completed Algebraic K-theory
• External Spanier-Whitehead duality and homology representation theorems for diagram spaces
• Orientable homotopy modules
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• Infinitesimal thickenings of Morava K-theories
• Formality of DG algebras (after Kaledin)
• A model category structure on the category of simplicial multicategories
• Koszul duality in exact categories
• Pursuing Lax Diagrams and Enrichment
• Left-induced model structures and diagram categories
• The enriched Thomason model structure on 2-categories
• Homotopy locally presentable enriched categories
• Homotopical finiteness of smooth and proper dg-algebras
• Braided injections and double loop spaces
• Homotopy in Exact Categories
• Tangent $\infty$-categories and Goodwillie calculus
• Reedy diagrams in V-model categories
• Correspondences and stable homotopy theory
• Enveloping operads and applications
• An algebraic model for rational S^1-equivariant stable homotopy theory
• A homotopy theory for enrichment in simplicial modules
• Axiomatic homotopy theory for operads
• Simplicial localization of monoidal structures, and a non-linear version of Deligne's conjecture
• On the homotopy theory of equivariant colored operads
• Categorical aspects of toric topology
• Monoidal cofibrant resolutions of dg algebras
• Differential calculus of Hochschild pairs for infinity-categories
• Spaces of Operad Structures
• Homotopy Theory of Bicomplexes
• The product formula in unitary deformation K-theory
• Realising ${\pi }_{\ast }^{e}R$-algebras by global ring spectra
• (Co)homology of Spectral Categories
• Verdier quotients of stable quasi-categories are localizations
• Extension DGAs and topological Hochschild homology
• Discrete G-Spectra and embeddings of module spectra
• Homotopy theory of presheaves of Gamma-spaces
• Admissible replacements for simplicial monoidal model categories
• Configuration spaces of clusters as $E_d$-algebras
• Adjoint associativity: an invitation to algebra in infinity-categories
• Toward a strictification theorem for co-Segal categories
• Generalized String Topology and Derived Koszul Duality
• Recollements induced by good silting objects
• $E_n$ ring spectra and Dyer-Lashof operations
• Higher symmetries in abstract stable homotopy theories
• Algebraic K-theory of finitely projective modules on ${\mathbb{E}}_{\infty }$-rings
• Spectral enrichments of model categories
• Modules over the de Rham cohomology spectrum
• On the moduli space of A-infinity structures
• Complements on enriched precategories
• Monoidal uniqueness theorems for stable homotopy theory
• Monoidality of Franke's Exotic Model
• An algebraic model for free rational G-spectra for connected compact Lie groups G
• Topological equivalences for differential graded algebras
• A Quillen model category structure on some categories of comonoids
• Lie coalgebras and rational homotopy theory, I: Graph coalgebras
• Classifying Rational G-Spectra for Finite G
• Homotopic Hopf-Galois extensions: foundations and examples
• Homology of I-adic towers
• Realizing modules over the homology of a DGA
• Monoidal Bousfield Localizations and Algebras over Operads: A User's Guide
• E-motives and motivic stable homotopy