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.

MSC Classifications:

18G30, 18F20, 55U35 show english descriptions Simplicial sets, simplicial objects (in a category) [See also 55U10]
Presheaves and sheaves [See also 14F05, 32C35, 32L10, 54B40, 55N30]
Abstract and axiomatic homotopy theory 18G30 - Simplicial sets, simplicial objects (in a category) [See also 55U10]
18F20 - Presheaves and sheaves [See also 14F05, 32C35, 32L10, 54B40, 55N30]
55U35 - Abstract and axiomatic homotopy theory

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