Lemma 13.9.3. Suppose that $f: K^\bullet \to L^\bullet $ and $g : L^\bullet \to M^\bullet $ are morphisms of complexes such that $g \circ f$ is homotopic to zero. Then

$g$ factors through a morphism $C(f)^\bullet \to M^\bullet $, and

$f$ factors through a morphism $K^\bullet \to C(g)^\bullet [-1]$.

## Comments (1)

Comment #291 by arp on