We construct the Bousfield-Kan completion with respect to a triple, for a model category. In the pointed case, we construct a Bousfield-Kan spectral sequence that computes the relative homotopy groups of the completion of an object.
These constructions are based on the existence of a diagonal for the cofibrant-replacement functor constructed using the small object argument.
A central result that we use, due to Dwyer, Kan and Hirschhorn, is that in a model category homotopy limits commute with the function complex. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Cofibrance; Completion; Localization; Simplicial; Subdivision
Title
Cofibrance and *completion
Author
Radulescu-Banu, Andrei
Source
DAI-B 60/10, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
Advisor
Miller, Haynes R.
University/institution
Massachusetts Institute of Technology
University location
United States -- Massachusetts
Source type
Dissertation or Thesis
Document type
Dissertation/Thesis
Dissertation/thesis number
0800615
ProQuest document ID
304555994
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/304555994