## Homology, Homotopy and Applications

- Homology Homotopy Appl.
- Volume 11, Number 1 (2009), 35-60.

### Homotopy theory of presheaves of Γ-spaces

#### 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.

#### Article information

**Source**

Homology Homotopy Appl., Volume 11, Number 1 (2009), 35-60.

**Dates**

First available in Project Euclid: 1 September 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.hha/1251832559

**Mathematical Reviews number (MathSciNet)**

MR2486652

**Zentralblatt MATH identifier**

1160.55007

**Subjects**

Primary: 55P47: Infinite loop spaces 55P42: Stable homotopy theory, spectra 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 55P48: Loop space machines, operads [See also 18D50]

**Keywords**

Model category homotopy theory simplicial presheaf infinite loop space

#### Citation

Bergsaker, Håkon Schad. Homotopy theory of presheaves of Γ-spaces. Homology Homotopy Appl. 11 (2009), no. 1, 35--60. https://projecteuclid.org/euclid.hha/1251832559