Rings, Modules, and Algebras in Stable Homotopy Theory (Repost)
A. D. Elmendorf, I. Kriz, M. A. Mandell, "Rings, Modules, and Algebras in Stable Homotopy Theory"
2007 | pages: 269 | ISBN: 0821843036, 0821806386 | PDF | 2 mb
2007 | pages: 269 | ISBN: 0821843036, 0821806386 | PDF | 2 mb
This book introduces a new point-set level approach to stable homotopy theory that has already had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum $S$, the authors construct an associative, commutative, and unital smash product in a complete and cocomplete category of ""$S$-modules"" whose derived category is equivalent to the classical stable homotopy category. This construction allows for a simple and algebraically manageable definition of ""$S$-algebras"" and ""commutative $S$-algebras"" in terms of associative, or associative and commutative, products $R\wedge SR \longrightarrow R$. These notions are essentially equivalent to the earlier notions of $A {\infty $ and $E {\infty $ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of $R$-modules in terms of maps $R\wedge SM\longrightarrow M$. When $R$ is commutative, the category of $R$-modules also has a
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