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

DOI:
https://doi.org/10.1090/S0894-0347-99-00320-3

Published electronically:
September 22, 1999

MathSciNet review:
1695653

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Abstract | References | Similar Articles | Additional Information

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, 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.

Article copyright:
© Copyright 1999
American Mathematical Society