Lemma 15.86.2. Let
be a short exact sequence of inverse systems of abelian groups. Then there is an associated 6 term exact sequence 0 \to \mathop{\mathrm{lim}}\nolimits A_ i \to \mathop{\mathrm{lim}}\nolimits B_ i \to \mathop{\mathrm{lim}}\nolimits C_ i \to R^1\mathop{\mathrm{lim}}\nolimits A_ i \to R^1\mathop{\mathrm{lim}}\nolimits B_ i \to R^1\mathop{\mathrm{lim}}\nolimits C_ i \to 0.
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