Definition 7.47.3. Let $\mathcal{C}$ be a category. Given a family of morphisms $\{ f_ i : U_ i \to U\} _{i\in I}$ of $\mathcal{C}$ with target $U$ we say the sieve $S$ on $U$ described in Lemma 7.47.2 part (4) is the sieve on $U$ generated by the morphisms $f_ i$.

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