Geodesic
Symmetric spectra
Hovey, Mark1 ; Shipley, Brooke2 ; Smith, Jeff
1Department of Mathematics, Wesleyan University, Middletown, Connectitut 06459
2Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Journal of the American Mathematical Society, Tome 13 (2000) no. 1, pp. 149-208
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The stable homotopy category, much studied by algebraic topologists, is a closed symmetric monoidal category. For many years, however, there has been no well-behaved closed symmetric monoidal category of spectra whose homotopy category is the stable homotopy category. In this paper, we present such a category of spectra; the category of symmetric spectra. Our method can be used more generally to invert a monoidal functor, up to homotopy, in a way that preserves monoidal structure. Symmetric spectra were discovered at about the same time as the category of $S$-modules of Elmendorf, Kriz, Mandell, and May, a completely different symmetric monoidal category of spectra.
DOI : 10.1090/S0894-0347-99-00320-3

Hovey, Mark  1   ; Shipley, Brooke  2   ; Smith, Jeff 

1 Department of Mathematics, Wesleyan University, Middletown, Connectitut 06459
2 Department of Mathematics, Purdue University, West Lafayette, Indiana 47907 
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Hovey, Mark; Shipley, Brooke; Smith, Jeff. Symmetric spectra. Journal of the American Mathematical Society, Tome 13 (2000) no. 1, pp. 149-208. doi: 10.1090/S0894-0347-99-00320-3

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