# 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}
}
• J. Jardine
• Published 2006
• Mathematics
• Homology, Homotopy and Applications
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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