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.

For $C$ a site and $SSh(C)$ the category of sheaves on $X$ with values in simplicial sets, Joyalâ€™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.

- J. F. Jardine, page 9 of:
*Fields lectures: simplicial presheaves*(pdf)

Last revised on June 12, 2021 at 20:04:12. See the history of this page for a list of all contributions to it.