Definition 7.1.1. A morphism \(f\colon X \to Y\) is called an \(E\)-equivalence if the induced map \(E \otimes f\colon E \otimes X \to E \otimes Y\) is an isomorphism. We say that a spectrum \(X\) is \(E\)-acyclic if the map \(X \to 0\) is an \(E\)-equivalence, i.e. if \(E \otimes X\) is the zero spectrum.
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