Definition 7.47.4. Let $\mathcal{C}$ be a category. Let $f : V \to U$ be a morphism of $\mathcal{C}$. Let $S \subset h_ U$ be a sieve. We define the pullback of $S$ by $f$ to be the sieve $S \times _ U V$ of $V$ defined by the rule

$(\alpha : T \to V) \in (S \times _ U V)(T) \Leftrightarrow (f \circ \alpha : T \to U) \in S(T)$

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