Lemma 12.32.1. Let I be a set. For i \in I let L_ i \to M_ i \to N_ i be a complex of abelian groups. Let H_ i = \mathop{\mathrm{Ker}}(M_ i \to N_ i)/\mathop{\mathrm{Im}}(L_ i \to M_ i) be the cohomology. Then
\prod L_ i \to \prod M_ i \to \prod N_ i
is a complex of abelian groups with homology \prod H_ i.
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