Stable Categories And Structured Ring Spectra
Download Stable Categories And Structured Ring Spectra PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Stable Categories And Structured Ring Spectra book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Stable Categories and Structured Ring Spectra
Author: Andrew J. Blumberg
language: en
Publisher: Cambridge University Press
Release Date: 2022-07-21
A graduate-level introduction to the homotopical technology in use at the forefront of modern algebraic topology.
Rings, Modules, and Algebras in Stable Homotopy Theory
Author: Anthony D. Elmendorf
language: en
Publisher: American Mathematical Soc.
Release Date: 1997
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
Structured Ring Spectra
Author: Andrew Baker
language: en
Publisher: Cambridge University Press
Release Date: 2004-11-18
This book contains some important new contributions to the theory of structured ring spectra.