Corollary 6.1.25. Given a \(k\)-connective complex \(A \in \D (\Aa )_{\geq k}\) and a \((k-1)\)-coconnective complex \(B \in \D (\Aa )_{\leq k-1}\), we have \[ \Hom _{\D (\Aa )}(A,B) = 0. \]
Proof. By adjunction we have \(\Hom _{\D (\Aa )}(A,B) \simeq \Hom _{\D (\Aa )}(A,\tau _{\geq k}B) = 0\), where we use that \(\tau _{\geq k}B = 0\) as its homology is trivial. □
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