# Idea

See model structure on simplicial presheaves for background, idea and introduction.

The local model structure on simplicial presheaves has a slight variant with presheaves replaced by sheaves.

This is originally due to Joyal. Later Jardine introduced the local model structure on simplicial presheaves and proved that both are Quillen equivalent.

# Definition

For $C$ a site and $SSh(C)$ the category of sheaves on $X$ with values in simplicial sets, Joyal’s local model structure on $SSh(X)$ is (from a revisionist point of view) the restriction of the injective local model structure on simplicial presheaves from all presheaves to sheaves.

# References

See page 9 of

• Jardine, Fields lectures: simplicial presheaves (pdf)
Created on June 30, 2009 19:09:52 by Urs Schreiber (134.100.222.156)