Pullback of sieve

Let \(f\colon X \to Y\) be a morphism in some category \(C\). For every sieve \(U \hookrightarrow y(Y)\), we denote by \(f^*U \hookrightarrow y(X)\) the sieve obtained by pullback along \(y(f)\colon y(X) \to y(Y)\). Note that it consists of those morphisms \(g\colon Z \to X\) such that the composite \(f \circ g\) is in the sieve \(U\).