The Stacks project

Lemma 12.14.5. Notation and assumptions as in Lemma 12.14.4 above. The morphism of complexes $\delta (s) : C_\bullet \to A[-1]_\bullet $ induces the maps

\[ H_ i(\delta (s)) : H_ i(C_\bullet ) \longrightarrow H_ i(A[-1]_\bullet ) = H_{i - 1}(A_\bullet ) \]

which occur in the long exact homology sequence associated to the short exact sequence of chain complexes by Lemma 12.13.6.

Proof. Omitted. $\square$

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