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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TLDR
The discussion by Dr. Hardy was intended to infer indirectly that by improving cerebral circulation, infarction can be prevented, and it is pleased that his work may help to elucidate this belief.
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