Homology, Homotopy and Applications

Volume 11 (2009)

Number 1

Homotopy theory of presheaves of Γ-spaces

Pages: 35 – 60

DOI: http://dx.doi.org/10.4310/HHA.2009.v11.n1.a3

Author

Håkon Schad Bergsaker (Department of Mathematics, University of Oslo, Norway)

Abstract

We consider the category of presheaves of Γ-spaces, or equivalently, of Γ-objects in simplicial presheaves. Our main result is the construction of stable model structures on this category parametrised by local model structures on simplicial presheaves. If a local model structure on simplicial presheaves is monoidal, then the corresponding stable model structure on presheaves of Γ-spaces is monoidal and satisfies the monoid axiom. This allows us to lift the stable model structures to categories of algebras and modules over a monoid.

Keywords

model category; homotopy theory; simplicial presheaf; infinite loop space

2010 Mathematics Subject Classification

55P42, 55P43, 55P47, 55P48

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