Axiomatic Stable Homotopy Theory

Axiomatic Stable Homotopy Theory
Author: Mark Hovey
Publisher: American Mathematical Soc.
Total Pages: 130
Release: 1997
Genre: Mathematics
ISBN: 0821806246


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We define and investigate a class of categories with formal properties similar to those of the homotopy category of spectra. This class includes suitable versions of the derived category of modules over a commutative ring, or of comodules over a commutative Hopf algebra, and is closed under Bousfield localization. We study various notions of smallness, questions about representability of (co)homology functors, and various kinds of localization. We prove theorems analogous to those of Hopkins and Smith about detection of nilpotence and classification of thick subcategories. We define the class of Noetherian stable homotopy categories, and investigate their special properties. Finally, we prove that a number of categories occurring in nature (including those mentioned above) satisfy our axioms.


Axiomatic Stable Homotopy Theory
Language: en
Pages: 130
Authors: Mark Hovey
Categories: Mathematics
Type: BOOK - Published: 1997 - Publisher: American Mathematical Soc.

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We define and investigate a class of categories with formal properties similar to those of the homotopy category of spectra. This class includes suitable versio
Axiomatic Stable Homotopy Theory Paperback
Language: en
Pages: 130
Authors: Mark Hovey
Categories: MATHEMATICS
Type: BOOK - Published: 2014-09-11 - Publisher: American Mathematical Society(RI)

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This work gives an axiomatic presentation of stable homotopy theory. It starts with axioms defining a stable homotopy category; using these axioms, one can make
Axiomatic, Enriched and Motivic Homotopy Theory
Language: en
Pages: 396
Authors: John Greenlees
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

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The NATO Advanced Study Institute "Axiomatic, enriched and rna tivic homotopy theory" took place at the Isaac Newton Institute of Mathematical Sciences, Cambrid
Equivariant Stable Homotopy Theory
Language: en
Pages: 548
Authors: L. Gaunce Jr. Lewis
Categories: Mathematics
Type: BOOK - Published: 2006-11-14 - Publisher: Springer

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This book is a foundational piece of work in stable homotopy theory and in the theory of transformation groups. It may be roughly divided into two parts. The fi
Memoirs of the American Mathematical Society
Language: en
Pages: 974
Authors:
Categories: Mathematics
Type: BOOK - Published: 1988 - Publisher:

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