Lemma 7.17.5. Let $\mathcal{C}$ be a site.

If $U \to V$ is a morphism of $\mathcal{C}$ such that $h_ U^\# \to h_ V^\# $ is surjective and $U$ is quasi-compact, then $V$ is quasi-compact.

If $\mathcal{F} \to \mathcal{G}$ is a surjection of sheaves of sets and $\mathcal{F}$ is quasi-compact, then $\mathcal{G}$ is quasi-compact.

## Comments (1)

Comment #7339 by Alejandro González Nevado on