Geodesic
Categorical homotopy theory
Homology, homotopy, and applications, Tome 8 (2006) no. 1, pp. 71-144.

Voir la notice de l'article provenant de la source International Press of Boston

This paper is an exposition of the ideas and methods of Cisinksi, in the context of $A$-presheaves on a small Grothendieck site, where $A$ is an arbitrary test category in the sense of Grothendieck. The homotopy theory for the category of simplicial presheaves and each of its localizations can be modelled by $A$-presheaves in the sense that there is a corresponding model structure for $A$-presheaves with an equivalent homotopy category. The theory specializes, for example, to the homotopy theories of cubical sets and cubical presheaves, and gives a cubical model for motivic homotopy theory. The applications of Cisinski’s ideas are explained in some detail for cubical sets.
DOI : 10.4310/HHA.2006.v8.n1.a3
Classification : 14F35, 18F20, 55P60
Keywords: test categories, weak equivalence classes, cubical sets and presheaves 
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J. F. Jardine. Categorical homotopy theory. Homology, homotopy, and applications, Tome 8 (2006) no. 1, pp. 71-144. doi : 10.4310/HHA.2006.v8.n1.a3. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2006.v8.n1.a3/

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