Definition 83.5.1. Let $S$ be a scheme, and let $B$ be an algebraic space over $S$. Let $j : R \to U \times _ B U$ be a pre-relation over $B$. If $u \in |U|$, then the orbit, or more precisely the $R$-orbit of $u$ is
\[ O_ u = \left\{ u' \in |U|\ : \begin{matrix} \exists n \geq 1, \ \exists u_0, \ldots , u_ n \in |U|\text{ such that } u_0 = u \text{ and } u_ n = u'
\\ \text{and for all }i \in \{ 0, \ldots , n - 1\} \text{ either } u_ i = u_{i + 1}\text{ or }
\\ \exists r \in |R|, \ s(r) = u_ i, t(r) = u_{i + 1} \text{ or }
\\ \exists r \in |R|, \ t(r) = u_ i, s(r) = u_{i + 1}
\end{matrix} \right\} \]
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Comment #3414 by Niels on
Comment #3476 by Johan on