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Search: MSC category 55U35 ( Abstract and axiomatic homotopy theory )

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1. CMB 2011 (vol 55 pp. 319)

Jardine, J. F.
The Verdier Hypercovering Theorem
This note gives a simple cocycle-theoretic proof of the Verdier hypercovering theorem. This theorem approximates morphisms $[X,Y]$ in the homotopy category of simplicial sheaves or presheaves by simplicial homotopy classes of maps, in the case where $Y$ is locally fibrant. The statement proved in this paper is a generalization of the standard Verdier hypercovering result in that it is pointed (in a very broad sense) and there is no requirement for the source object $X$ to be locally fibrant.

Keywords:simplicial presheaf, hypercover, cocycle
Categories:14F35, 18G30, 55U35

2. CMB 2006 (vol 49 pp. 407)

Jardine, J. F.
Intermediate Model Structures for Simplicial Presheaves
This note shows that any set of cofibrations containing the standard set of generating projective cofibrations determines a cofibrantly generated proper closed model structure on the category of simplicial presheaves on a small Grothendieck site, for which the weak equivalences are the local weak equivalences in the usual sense.

Categories:18G30, 18F20, 55U35

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