Cosimplicial resolutions and homotopy spectral sequences in model categories

By AK Bousfield. 2003

90 citations recorded by the source corpus.

We develop a general theory of cosimplicial resolutions, homotopy spectral sequences, and completions for objects in model categories, extending work of Bouseld{Kan and Bendersky{Thompson for ordinary spaces. This is based on a generalized cosimplicial version of the Dwyer{Kan{Stover theory of resolution model categories, and we are able to construct our homotopy spectral sequences and completions using very flexible weak resolutions in the spirit of relative homological algebra. We deduce that our completion functors have triple structures and preserve certain ber squares up to homotopy. We also deduce that the Bendersky{Thompson completions over connective ring spectra are equivalent to Bouseld{Kan completions over solid rings. The present work allows us to show, in a subsequent paper, that the homotopy spectral sequences over arbitrary ring spectra have well-behaved composition pairings.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/da873ad03486c81f07f137434ca6b22936aa6acd

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Citations in the corpus

Model Categories and Simplicial Methods (2006, background): “Both assumptions are unnecessary, as explained in [5], and can be removed at the cost of ramping up the language.”
Structured Ring Spectra: Moduli spaces of commutative ring spectra (2004, background): “The following ideas are straight out of Bousfield's paper [9] is onto for all P-epi maps.”