The Stacks project

Definition 103.17.2. Let $\mathcal{X}$ be a locally Noetherian algebraic stack. An $\mathcal{O}_\mathcal {X}$-module $\mathcal{F}$ is called coherent if $\mathcal{F}$ satisfies one (and hence all) of the equivalent conditions of Lemma 103.17.1. The category of coherent $\mathcal{O}_\mathcal {X}$-modules is denote $\textit{Coh}(\mathcal{O}_\mathcal {X})$.