Sheaf of spectra

In algebraic topology, a presheaf of spectra on a topological space "X" is a contravariant functor from the category of open subsets of "X", where morphisms are inclusions, to the good category of commutative ring spectra. A theorem of Jardine says that such presheaves form a simplicial model category, where "F" →"G" is a weak equivalence if the induced map of homotopy sheaves formula_1 is an isomorphism. A sheaf of spectra is then a fibrant/cofibrant object in that category.
The notion is used to define, for example, a derived scheme in algebraic geometry.