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Intermediate model structures for simplicial presheaves. (English) Zbl 1107.18007

This note presents a proper closed model structure on the category of simplicial presheaves on a small Grothendieck site intermediate between the local projective model structure [cf. B. Blander, \(K\)-theory 24, 283–301 (2001; Zbl 1073.14517)] and the standard one [cf. J. F. Jardine, J. Pure Appi. Algebra 47, 35–87 (1987; Zbl 0624.18007)]. That is determined by any set of cofibrations containing the standard set of generating projective cofibrations. The weak equivalences are the local weak equivalences in the usual sense. The presented structure is shown to be cofibrantly generated.

MSC:

18G30 Simplicial sets; simplicial objects in a category (MSC2010)
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
55U35 Abstract and axiomatic homotopy theory in algebraic topology
14F35 Homotopy theory and fundamental groups in algebraic geometry
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