Cofibrance and Completion
Abstract
Description
For a cofibrantly generated Quillen model category, we show that the cofibrant replacement functor constructed using the small object argument admits a cotriple structure. If all acyclic cofibrations are monomorphisms, the fibrant replacement functor constructed using the small object argument admits a triple structure. For a triple in the base category, the associated cosimplicial resolution is not necessarily homotopy invariant. However using a mix of the triple with the cofibrant replacement cotriple we construct a 'homotopically correct' version of the cosimplicial resolution of the triple. This allows us to construct a Bousfield-Kan completion functor with respect to a triple, and for pointed cofibrantly-generated model categories a Bousfield-Kan spectral sequence that computes the relative homotopy groups of the Bousfield-Kan completion of an object.
This is the text of my PhD thesis, worked under the supervision of Prof. Haynes Miller, submitted on Feb. 1999 at MIT.
This is the text of my PhD thesis, worked under the supervision of Prof. Haynes Miller, submitted on Feb. 1999 at MIT. Ams-latex, 67 pages
This is the text of my PhD thesis, worked under the supervision of Prof. Haynes Miller, submitted on Feb. 1999 at MIT. Ams-latex, 67 pages