Lemma 7.10.4. The association $\mathcal{F} \mapsto (\mathcal{F} \to \mathcal{F}^+)$ is a functor.

**Proof.**
Instead of proving this we state exactly what needs to be proven. Let $\mathcal{F} \to \mathcal{G}$ be a map of presheaves. Prove the commutativity of:

\[ \xymatrix{ \mathcal{F} \ar[r] \ar[d] & \mathcal{F}^{+} \ar[d] \\ \mathcal{G} \ar[r] & \mathcal{G}^{+} } \]

$\square$
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