Corollary 6.4.5. Let \(\Aa \) be an abelian category and let \(M\in \Aa \) be projective. Then for every \(X\in \D (\Aa )\) and every \(n\in \Z \), there is a natural isomorphism \[ \pi _n\hom _{\D (\Aa )}(M[0],X)\cong \Hom _{\Aa }(M,H_n(X)). \]
Proof. This is the computation in the second half of the proof of Lemma 6.4.4. □
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