The Stacks project

Situation 69.5.5. Let $S$ be a scheme. Let $X = \mathop{\mathrm{lim}}\nolimits _{i \in I} X_ i$ be the limit of a directed inverse system of algebraic spaces over $S$ with affine transition morphisms (Lemma 69.4.1). We assume that $X_ i$ is quasi-compact and quasi-separated for all $i \in I$. We also choose an element $0 \in I$.

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