The Stacks project

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:

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

Comments (1)

Comment #8569 by Alejandro González Nevado on

SS: The association sending a presheaf to the map of presheaves sending this presheaf to its zeroth Čech cohomology is a functor.

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  • 8 comment(s) on Section 7.10: Sheafification

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