Rings, Modules, and Algebras in Stable Homotopy Theory
Regular price
€122.99
A01=A.D. Elmendorf
A01=I. Kriz
A01=J.Peter May
A01=M. Cole
A01=M.A. Mandell
Author_A.D. Elmendorf
Author_I. Kriz
Author_J.Peter May
Author_M. Cole
Author_M.A. Mandell
Category=PBG
Category=PBPD
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Product details
- ISBN 9780821843031
- Weight: 482g
- Publication Date: 30 Apr 2007
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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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
