Lemma 13.9.17. Let $\mathcal{A}$ be an additive category. Let $f : K^\bullet \to L^\bullet$ be a morphism of complexes. The triangle $(L^\bullet , C(f)^\bullet , K^\bullet [1], i, p, f[1])$ is the triangle associated to the termwise split sequence

$0 \to L^\bullet \to C(f)^\bullet \to K^\bullet [1] \to 0$

coming from the definition of the cone of $f$.

Proof. Immediate from the definitions. $\square$

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