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A sheaf-theoretic view of loop spaces

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Mark W. Johnson

The context of enriched sheaf theory introduced in the author's thesis
provides a convenient viewpoint for models of the stable homotopy
category as well as categories of finite loop spaces.
Also, the languages
of algebraic geometry and algebraic topology have been interacting
quite heavily in recent years, primarily due to the work of
Voevodsky and that of Hopkins. Thus, the language of Grothendieck
topologies is becoming a necessary tool for the algebraic topologist.
The current article is intended to give a somewhat relaxed
introduction to this language of sheaves in a topological
context, using familiar examples such as n-fold loop spaces and
pointed G-spaces. This language also includes the
diagram categories of spectra
as well as spectra in the sense
of Lewis, which will be discussed in some detail.

Keywords: loop spaces, spectra, Quillen closed model categories, enriched sheaves.

2000 MSC: 55P42, 18F20, 18G55, 55P35.

*Theory and Applications of Categories*, Vol. 8, 2001, No. 19, pp 490-508.

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