Lemma 12.14.11. Notation and assumptions as in Lemma 12.14.10 above. Assume in addition that $\mathcal{A}$ is abelian. The morphism of complexes $\delta : C^\bullet \to A[1]^\bullet$ induces the maps

$H^ i(\delta ) : H^ i(C^\bullet ) \longrightarrow H^ i(A[1]^\bullet ) = H^{i + 1}(A^\bullet )$

which occur in the long exact homology sequence associated to the short exact sequence of cochain complexes by Lemma 12.13.12.

Proof. Omitted. $\square$

Comment #2795 by Tim on

Is there a reference, where the proof is carried out in detail?

There are also:

• 2 comment(s) on Section 12.14: Homotopy and the shift functor

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