# 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
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.

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