The Stacks project

Remark 70.23.5. In Situation 70.23.1 Lemmas 70.23.2, 70.23.3, and 70.23.4 tell us that the category of algebraic spaces quasi-separated and of finite type over $B$ is equivalent to certain types of inverse systems of algebraic spaces over $(B_ i)_{i \in I}$, namely the ones produced by applying Lemma 70.23.3 to a diagram of the form ( For example, given $X \to B$ finite type and quasi-separated if we choose two different diagrams $X \to V_1 \to B_{i_1}$ and $X \to V_2 \to B_{i_2}$ as in (, then applying Lemma 70.23.4 to $\text{id}_ X$ (in two directions) we see that the corresponding limit descriptions of $X$ are canonically isomorphic (up to shrinking the directed set $I$). And so on and so forth.

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