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Equivariant orthogonal spectra and Smodules
 MR1922205 (2003i:55012), Zbl 1025.55002
"... 1. Right exact functors on categories of diagram spaces 2 2. The proofs of the comparison theorems 5 3. The construction of the functor N ∗ 12 ..."
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Cited by 111 (13 self)
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1. Right exact functors on categories of diagram spaces 2 2. The proofs of the comparison theorems 5 3. The construction of the functor N ∗ 12
A convenient model category for commutative ring spectra
, 2003
"... We develop a new system of model structures on the modules, algebras and commutative algebras over symmetric spectra. In addition to the same properties as the standard stable model structures defined in [HSS] and [MMSS], these model structures have better compatibility properties between commutati ..."
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Cited by 70 (5 self)
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We develop a new system of model structures on the modules, algebras and commutative algebras over symmetric spectra. In addition to the same properties as the standard stable model structures defined in [HSS] and [MMSS], these model structures have better compatibility properties between commutative algebras and the underlying modules.
HZalgebra spectra are differential graded algebras
 Amer. Jour. Math
, 2004
"... Abstract: We show that the homotopy theory of differential graded algebras coincides with the homotopy theory of HZalgebra spectra. Namely, we construct Quillen equivalences between the Quillen model categories of (unbounded) differential graded algebras and HZalgebra spectra. We also construct Qu ..."
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Cited by 67 (16 self)
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Abstract: We show that the homotopy theory of differential graded algebras coincides with the homotopy theory of HZalgebra spectra. Namely, we construct Quillen equivalences between the Quillen model categories of (unbounded) differential graded algebras and HZalgebra spectra. We also construct Quillen equivalences between the differential graded modules and module spectra over these algebras. We use these equivalences in turn to produce algebraic models for rational stable model categories. We show that bascially any rational stable model category is Quillen equivalent to modules over a differential graded Qalgebra (with many objects). 1.
Equivalences of monoidal model categories
 Algebr. Geom. Topol
, 2002
"... Abstract: We construct Quillen equivalences between the model categories of monoids (rings), modules and algebras over two Quillen equivalent model categories under certain conditions. This is a continuation of our earlier work where we established model categories of monoids, modules and algebras [ ..."
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Cited by 52 (12 self)
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Abstract: We construct Quillen equivalences between the model categories of monoids (rings), modules and algebras over two Quillen equivalent model categories under certain conditions. This is a continuation of our earlier work where we established model categories of monoids, modules and algebras [SS00]. As an application we extend the DoldKan equivalence to show that the model categories of simplicial rings, modules and algebras are Quillen equivalent to the associated model categories of connected differential graded rings, modules and algebras. We also show that our classification results from [SS] concerning stable model categories translate to any one of the known symmetric monoidal model categories of spectra. 1.
Morita theory in abelian, derived and stable model categories, Structured ring spectra
 London Math. Soc. Lecture Note Ser
, 2004
"... These notes are based on lectures given at the Workshop on Structured ring spectra and ..."
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Cited by 27 (0 self)
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These notes are based on lectures given at the Workshop on Structured ring spectra and
A uniqueness theorem for stable homotopy theory
 Math. Z
, 2002
"... Roughly speaking, the stable homotopy category of algebraic topology is obtained from the ..."
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Cited by 23 (10 self)
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Roughly speaking, the stable homotopy category of algebraic topology is obtained from the
Homotopy theory of modules over operads in symmetric spectra
, 2009
"... We establish model category structures on algebras and modules over operads in symmetric spectra, and study when a morphism of operads induces a Quillen equivalence between corresponding categories of algebras (resp. modules) over operads. ..."
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Cited by 16 (2 self)
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We establish model category structures on algebras and modules over operads in symmetric spectra, and study when a morphism of operads induces a Quillen equivalence between corresponding categories of algebras (resp. modules) over operads.
Operads and Chain Rules for the Calculus of Functors
"... Abstract. We study the structure possessed by the Goodwillie derivatives of a pointed homotopy functor of based topological spaces. These derivatives naturally form a bimodule over the operad consisting of the derivatives of the identity functor. We then use these bimodule structures to give a chain ..."
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Cited by 14 (3 self)
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Abstract. We study the structure possessed by the Goodwillie derivatives of a pointed homotopy functor of based topological spaces. These derivatives naturally form a bimodule over the operad consisting of the derivatives of the identity functor. We then use these bimodule structures to give a chain rule for higher derivatives in the calculus of functors, extending that of Klein and Rognes. This chain rule expresses the derivatives of FG as a derived composition product of the derivatives of F and G over the derivatives of the identity. There are two main ingredients in our proofs. Firstly, we construct new models for the Goodwillie derivatives of functors of spectra. These models allow for natural composition maps that yield operad and module structures. Then, we use a cosimplicial cobar construction to transfer this structure to functors of topological spaces. A form of Koszul duality for operads of spectra plays a key role in this. In a landmark series of papers, [16], [17] and [18], Goodwillie outlines his ‘calculus of homotopy functors’. Let F: C → D (where C and D are each either Top ∗, the category of pointed topological spaces, or Spec, the category of spectra) be a pointed homotopy functor. One of the things that Goodwillie does is associate with F a sequence of spectra, which are called the derivatives of F.