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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Symmetric spectra


Authors: Mark Hovey, Brooke Shipley and Jeff Smith
Journal: J. Amer. Math. Soc. 13 (2000), 149-208
MSC (2000): Primary 55P42, 55U10, 55U35
Published electronically: September 22, 1999
MathSciNet review: 1695653
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Abstract: 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.


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Additional Information

Mark Hovey
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: hovey@member.ams.org

Brooke Shipley
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: bshipley@math.purdue.edu

Jeff Smith
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: jhs@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-99-00320-3
PII: S 0894-0347(99)00320-3
Received by editor(s): March 31, 1998
Received by editor(s) in revised form: July 7, 1999
Published electronically: September 22, 1999
Additional Notes: The first two authors were partially supported by NSF Postdoctoral Fellowships
The third author was partially supported by an NSF Grant.
Article copyright: © Copyright 1999 American Mathematical Society