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 |
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