Definition 102.17.2. 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 102.17.1. The category of coherent $\mathcal{O}_\mathcal {X}$-modules is denote $\textit{Coh}(\mathcal{O}_\mathcal {X})$.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).