Lemma 15.28.8. Let $R$ be a ring. Let $f_1, \ldots , f_ r$ be a sequence of elements of $R$. The complex $K_\bullet (f_1, \ldots , f_ r)$ is isomorphic to the cone of the map of complexes

$f_ r : K_\bullet (f_1, \ldots , f_{r - 1}) \longrightarrow K_\bullet (f_1, \ldots , f_{r - 1}).$

Proof. Special case of Lemma 15.28.7. $\square$

## Comments (2)

Comment #2447 by Raymond Cheng on

Should be $f_r \colon K_\bullet(f_1,\ldots,f_{r-1}) \to K_\bullet(f_1,\ldots,f_{r-1})$ instead of $f_n\colon K_\bullet(f_1,\ldots,f_{r-1}) \to K_\bullet(f_1,\ldots,f_{r-1})$.

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