nLab
local model structure on simplicial sheaves

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 CC a site and SSh(C)SSh(C) the category of sheaves on XX with values in simplicial sets, Joyal’s local model structure on SSh(X)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)