Lemma 86.3.5. Let $R$ be a ring. Let $M^\bullet$ be a two term complex $M^{-1} \to M^0$ over $R$. If $\varphi , \psi \in \text{End}_{D(R)}(M^\bullet )$ are zero on $H^ i(M^\bullet )$, then $\varphi \circ \psi = 0$.

Proof. Apply Derived Categories, Lemma 13.12.5 to see that $\varphi \circ \psi$ factors through $\tau _{\leq -2}M^\bullet = 0$. $\square$

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