# CATEGORICAL HOMOTOPY THEORY

@article{Jardine2006CATEGORICALHT, title={CATEGORICAL HOMOTOPY THEORY}, author={John F. Jardine}, journal={Homology, Homotopy and Applications}, year={2006}, volume={8}, pages={71-144} }

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…

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