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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 $k \geq c$.

Comments (2)

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 -functor is exact if one works with the abelian category of abelian sheaves on a site. Isn't it true that is not just in the ├ętale 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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