Homological Localisation of Model Categories

One of the most useful methods for studying the stable homotopy category is localising at some spectrum E. For an arbitrary stable model category we introduce a candidate for the E–localisation of this model category. We study the properties of this new construction and relate it to some well–known categories.

[1]  Douglas C. Ravenel,et al.  Nilpotence and Periodicity in Stable Homotopy Theory. , 1992 .

[2]  B. Shipley,et al.  Algebras and Modules in Monoidal Model Categories , 1998, math/9801082.

[3]  R. Tennant Algebra , 1941, Nature.

[4]  Philip S. Hirschhorn Model categories and their localizations , 2003 .

[5]  ENRICHED MODEL CATEGORIES AND AN APPLICATION TO ADDITIVE ENDOMORPHISM SPECTRA , 2006, math/0602107.

[6]  S. Schwede The stable homotopy category is rigid , 2007 .

[7]  J. Bergner Homotopy fiber products of homotopy theories , 2008, 0811.3175.

[8]  Symmetric spectra , 1998, math/9801077.

[9]  Mark Hovey,et al.  Morava K-theories and localisation , 1999 .

[10]  Constanze Roitzheim,et al.  STABLE LEFT AND RIGHT BOUSFIELD LOCALISATIONS , 2012, Glasgow Mathematical Journal.

[11]  B. Shipley,et al.  Stable model categories are categories of modules , 2003 .

[12]  B. M. Fulk MATH , 1992 .

[13]  Fabian Lenhardt Stable Frames in Model Categories , 2010, 1002.2837.

[14]  Michael Cole,et al.  Rings, Modules, and Algebras in Stable Homotopy Theory , 2007 .

[15]  Javier J. Gutiérrez Homological localizations of Eilenberg–MacLane spectra , 2005, math/0511412.

[16]  Constanze Roitzheim,et al.  Local Framings , 2011, 1103.0400.

[17]  Stefan Friedrich,et al.  Topology , 2019, Arch. Formal Proofs.

[18]  Paul G. Goerss,et al.  Simplicial Homotopy Theory , 2009, Modern Birkhäuser Classics.

[19]  Spectra and symmetric spectra in general model categories , 2000, math/0004051.

[20]  A. K. Bousfield The localization of spectra with respect to homology , 1975 .

[21]  Constanze Roitzheim Rigidity and exotic models for the K -local stable homotopy category , 2007 .

[22]  Bret Tilson Modules , 2010, Int. J. Algebra Comput..