Definition 7.1.3. A spectrum \(L\) is called \(E\)-local if for every \(E\)-equivalence \(f\colon X \to Y\), the induced map \(f^*\colon \hom (Y,L) \to \hom (X,L)\) on mapping spectra is an isomorphism. We denote by \[ \Sp _E \subseteq \Sp \] the full subcategory spanned by the \(E\)-local spectra.
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