nLab
model structure on cubical presheaves

Idea

Given a site, there is a model category structure on the category of cubical objects in the presheaf topos over that site, hence on the category of cubical set-valued presheaves, such that at least the corresponding homotopy category is equivalent to that of the corresponding local model structure on simplicial presheaves (Jardine 03, theorem 71) (the latter being known to present the (infinity,1)-topos over the given site).

Related concepts

• model structure on simplicial presheaves

• model structure on simplicial sheaves

• model structure on presheaves of spectra

• model structure for (2,1)-sheaves

References

• Rick Jardine, Categorical homotopy theory, 2003 (web)