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Journal of the American Mathematical Society

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ISSN 1088-6834 (online) ISSN 0894-0347 (print)

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Symmetric spectra
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by Mark Hovey, Brooke Shipley and Jeff Smith
J. Amer. Math. Soc. 13 (2000), 149-208
Published electronically: September 22, 1999


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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Bibliographic Information
  • Mark Hovey
  • Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connectitut 06459
  • Email:
  • Brooke Shipley
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • Email:
  • Jeff Smith
  • Email:
  • 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.
  • © Copyright 1999 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 13 (2000), 149-208
  • MSC (2000): Primary 55P42, 55U10, 55U35
  • DOI:
  • MathSciNet review: 1695653