Stable model categories are categories of modules

By S. Schwede, B. Shipley. 2003

340 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/7533761348db7a61de5cc72454df7c81fb7a9d01

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Citations in the corpus

A universal characterization of higher algebraic K-theory (2010, background): “The proof of the theorem establishes an ∞-categorical version of the Morita theory of [51]; that is, small stable idempotent-complete ∞-categories are categories of modules, and the ∞category of exact functors between two such is a stable subcategory of the category of bimodules.”
Derived Categories (2016, background): “For more information on these topics see [68], [135], [136], [100] and [38].”
Global Homotopy Theory (2018, methodology): “As an application of Morita theory for stable model categories [134], we can then deduce that rationally the global homotopy category for finite groups has an algebraic model, namely the derived category of rational global functors (Theorem IV.”
Models of G–spectra as presheaves of spectra (2011, background): “t model structures takes a fair amount of work. The original version was due to Lewis and May [11] and more modern versions that we shall start from are given in [12]. A result of Schwede and Shipley [20], reproven in [5], asserts that any stable model categoryM is equivalent to a category Pre(D,S) ”
Derived Algebraic Geometry III: Commutative Algebra (2007, background): “(F1) The model category A satisfies the monoid axiom of [73]: if U denotes the weakly saturated class generated by morphisms of the form idX ⊗f , where f is a trivial cofibration in A, then every morphism in U is a weak equivalence in A.”
The special fiber of the motivic deformation of the stable homotopy category is algebraic (2018, background): “For example, Schwede and Shipley [55] studied the case for the Eilenberg-Mac Lane spectrum HR, where R is a commutative ring, Patchkoria [50] studied the case for the complex periodic K-theory localized at an odd prime, Greenlees [18] studied the case for the rational S(1)-equivarant sphere spectrum”
Morita theory in abelian, derived and stable model categories (2003, methodology): “ectrum of (R ×n)f, M n(R) = End R((R ×n)f) . MORITA THEORY 31 The stable equivalence type of the matrix ring spectrum M n(R) is independent of the choice of ﬁbrant replacement, see Corollary A.2.4 of [SS03]. Moreover, the underlying spectrum of M n(R) is isomorphic, in the stable homotopy category, ”
Derived Algebraic Geometry II: Noncommutative Algebra (2007, positive): “For a proof in the language of model categories, we refer the reader to [61].”