## Symmetric spectra

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Mark Hovey, Brooke Shipley and Jeff Smith
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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.## References

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## Additional Information

**Mark Hovey**- Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connectitut 06459
- Email: hovey@member.ams.org
**Brooke Shipley**- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- Email: bshipley@math.purdue.edu
**Jeff Smith**- Email: jhs@math.purdue.edu
- 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: https://doi.org/10.1090/S0894-0347-99-00320-3
- MathSciNet review: 1695653