In topology loop spaces can be understood combinatorially using algebraic theories.
This approach can be extended to work for certain model structures on categories
of presheaves over a site with functorial unit interval objects, such as topological
spaces and simplicial sheaves of smooth schemes at finite type. For such model categories
a new category of algebraic theories with a proper cellular simplicial model
structure can be defined. This model structure can be localized in a way compatible
with left Bousfield localizations of the underlying category of presheaves to yield a
Motivic model structure for algebraic theories. As in the topological context, the
model structure is Quillen equivalent to a category of loop spaces in the underlying
category.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-1808 |
| Date | 02 June 2009 |
| Creators | Decker, Marvin Glen |
| Contributors | Lima-Filho, Paulo |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | electronic, application/pdf, born digital |
Page generated in 0.002 seconds