Lemma 34.8.17. Given schemes $X$, $Y$, $Y$ in $(\mathit{Sch}/S)_{ph}$ and morphisms $f : X \to Y$, $g : Y \to Z$ we have $g_{big} \circ f_{big} = (g \circ f)_{big}$.

**Proof.**
This follows from the simple description of pushforward and pullback for the functors on the big sites from Lemma 34.8.16.
$\square$

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