Remark 69.23.5. In Situation 69.23.1 Lemmas 69.23.2, 69.23.3, and 69.23.4 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 69.23.3 to a diagram of the form (69.23.2.1). 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 (69.23.2.1), then applying Lemma 69.23.4 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.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).