The Stacks project

Lemma 62.13.2. If $U \subset X$ and $V \subset Y$ are open and $f(U) \subset V$, then $(\alpha \circ \beta )|_ U$ is equal to $\alpha |_ U \circ \beta |_ V$.

Proof. Omitted. Hint: on fibres use Lemma 62.11.2. $\square$

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