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- Title
Cellularization of structures in stable homotopy categories.
- Authors
GUTIÉRREZ, JAVIER J.
- Abstract
We describe the formal framework for cellularization functors in triangulated categories and study the preservation of ring and module structures under these functors in stable homotopy categories in the sense of Hovey, Palmieri and Strickland, such as the homotopy category of spectra or the derived category of a commutative ring. We prove that cellularization functors preserve modules over connective rings but they do not preserve rings in general (even if the ring is connective or the cellularization functor is triangulated). As an application of these results, we describe the cellularizations of Eilenberg–Mac Lane spectra and compute all acyclizations in the sense of Bousfield of the integral Eilenberg–Mac Lane spectrum.
- Subjects
HOMOTOPY groups; CATEGORIES (Mathematics); EILENBERG-Moore spectral sequences; ACYCLIC model; HOMOTOPY theory; MATHEMATICAL proofs
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2012, Vol 153, Issue 3, p399
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004112000278