Lemma 7.25.7. Let $\mathcal{C}$ be a site. Let $U \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$. For any sheaf $\mathcal{F}$ on $\mathcal{C}$ we have $j_{U!}j_ U^{-1}\mathcal{F} = \mathcal{F} \times h_ U^\# $.

**Proof.**
This is clear from the description of $j_{U!}$ in Lemma 7.25.2.
$\square$

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