nLab model site

Idea

The notion of model site is a model category model for the notion of (∞,1)-site.

An (∞,1)-category equipped with the structure of a site on its homotopy category serves as a domain for ∞-stacks. It may be modeled by a model category.

A model category with a site structure on its homotopy category is called a pseudo model site (def 4.1.1 in ToVeI).

Examples

• The model structure on simplicial algebras equipped with the covering of the etale (infinity,1)-site.

Related concepts

• site

• 2-site

• (∞,1)-site

  • model site, simplicial site

  • model topos

References

• Bertrand Toën, Gabriele Vezzosi, Homotopical Algebraic Geometry I: Topos theory (arXiv)