Definition 4.4.31 (\(E\)-homology). Let \(E\) be a spectrum and let \(X \in \An _*\) be a pointed anima. For \(k\in \Z \), we define the reduced \(E\)-homology of \(X\) by \[ \widetilde E_k(X):=\pi _k(\Sigma ^{\infty }X\otimes E). \]
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