Exercise 4.3.28. In the situation of Lemma 4.3.22, use the prespectrum model to verify directly that for any spectrum \(Y \in \Sp (C)\) and any pointed object \(X \in C_*\) there is a natural isomorphism \[ \Hom _{\Sp (C)}(\Sigma ^{\infty }X, Y) \iso \Hom _{C_*}(X,\Omega ^{\infty }Y). \]
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