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
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.
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