nLab model structure on presheaves over a test category

Idea

For $C$ a test category, the canonical structure of a category with weak equivalences on the category of presheaves over $C$ lifts to the structure of a model category. All of these are models for the standard homotopy theory (the homotopy category of ∞Grpd).

Examples

• model structure on simplicial sets

• model structure on cubical sets

References

The model structure is due to

• Denis-Charles Cisinski, Les préfaisceaux comme type d'homotopie, Asterisque 308, (pdf).

Further developments are in

• Rick Jardine, Categorical homotopy theory, Homot. Homol. Appl. 8 (1), 2006, pp.71–144, (HHA, pdf).