Symmetric spectra |
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Authors: | Mark Hovey Brooke Shipley Jeff Smith |
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Affiliation: | Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459 ; Department of Mathematics, Purdue University, West Lafayette, Indiana 47907 ; Department of Mathematics, Purdue University, West Lafayette, Indiana 47907 |
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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 -modules of Elmendorf, Kriz, Mandell, and May, a completely different symmetric monoidal category of spectra. |
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