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2006 Categorical homotopy theory
J. F. Jardine
Homology Homotopy Appl. 8(1): 71-144 (2006).

Abstract

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.

Citation

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J. F. Jardine. "Categorical homotopy theory." Homology Homotopy Appl. 8 (1) 71 - 144, 2006.

Information

Published: 2006
First available in Project Euclid: 15 February 2006

zbMATH: 1087.18009
MathSciNet: MR2205215

Subjects:
Primary: 14F35 , 18F20 , 55P60

Rights: Copyright © 2006 International Press of Boston

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