Definition 21.31.2. Let $\{ f_ i : X_ i \to X\} $ be a family of morphisms with fixed target in the category $\textit{LC}$. We say this family is a qc covering1 if for every $x \in X$ there exist $i_1, \ldots , i_ n \in I$ and quasi-compact subsets $E_ j \subset X_{i_ j}$ such that $\bigcup f_{i_ j}(E_ j)$ is a neighbourhood of $x$.
[1] This is nonstandard notation. We chose it to remind the reader of fpqc coverings of schemes.
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