Definition 10.85.1. Let $(A_ i, \varphi _{ji})$ be a directed inverse system of sets over $I$. Then we say $(A_ i, \varphi _{ji})$ is Mittag-Leffler if for each $i \in I$, the family $\varphi _{ji}(A_ j) \subset A_ i$ for $j \geq i$ stabilizes. Explicitly, this means that for each $i \in I$, there exists $j \geq i$ such that for $k \geq j$ we have $\varphi _{ki}(A_ k) = \varphi _{ji}( A_ j)$. If $(A_ i, \varphi _{ji})$ is a directed inverse system of modules over a ring $R$, we say that it is Mittag-Leffler if the underlying inverse system of sets is Mittag-Leffler.

Comment #2970 by on

(1) Replace \it{Mittag-Leffler inverse system} by \it{Mittag-Leffler}. (2) (cf. Comment 2969) "the decreasing family ... stabilizes" seems a bit confusing. Maybe "the decreasingly directed family ... of subsets (or submodules) of $A_i$ attends its infimum"?

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