Axiomatic stable homotopy theory
by Hovey, Mark
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 a…
Read More ↓Title Statements
- Full title :Axiomatic stable homotopy theory / Mark Hovey, John H. Palmieri, Neil P. Strickland.
Summary
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.
Read More ↓Edition Statements
- Publication Date:©1997.
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, R.I
- Language:eng
- Publication Date:©1997.
Notes
"July 1997, volume 128, number 610 (second of 4 numbers)."
The Physical Object
- Description:ix, 114 pages : : illustrations ; : 26 cm.
Edition Identifiers
- ISBN:0821806246, 9780821806241
- oclc:ocm36573826
- LC Classification:QA3
- Dewey Decimal:510 s
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