Definition 12.31.2. Let $\mathcal{C}$ be an abelian category. We say the inverse system $(A_ i)$ satisfies the Mittag-Leffler condition, or for short is ML, if for every $i$ there exists a $c = c(i) \geq i$ such that

$\mathop{\mathrm{Im}}(A_ k \to A_ i) = \mathop{\mathrm{Im}}(A_ c \to A_ i)$

for all $k \geq c$.

Comment #7849 by DatPham on

I am a bit confused by the sentence following the above definition, namely that the Mittag-Leffler condition ensures that the $\lim$-functor is exact if one works with the abelian category of abelian sheaves on a site. Isn't it true that $R\lim \mathbf{Z}/l^n$ is not just $\mathbf{Z}_l$ in the étale topos?

Comment #8071 by on

Yes, I am confused too. THanks for catching this. I have fixed it and made the discussion slightly more precise here.

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