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Finite copoducts of sheaves conserve quasi-compactness.

Lemma 7.17.6. Let $\mathcal{C}$ be a site. If $n \geq 1$ and $\mathcal{F}_1, \ldots , \mathcal{F}_ n$ are quasi-compact sheaves on $\mathcal{C}$, then $\coprod _{i = 1, \ldots , n} \mathcal{F}_ i$ is quasi-compact.

Proof. Omitted. $\square$

Comments (1)

Comment #7340 by Alejandro González Nevado on

Slogan suggestion: finite copoducts of sheaves conserve quasi-compactness.

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