The Stacks project

Lemma 18.24.1. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $\theta : \mathcal{G} \to \mathcal{F}$ be a surjective $\mathcal{O}$-module map with $\mathcal{F}$ of finite presentation and $\mathcal{G}$ of finite type. Then $\mathop{\mathrm{Ker}}(\theta )$ is of finite type.

Proof. Omitted. Hint: See Modules, Lemma 17.11.3. $\square$

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