Definition 46.5.7. Let $S$ be a scheme. The category of adequate $\mathcal{O}$-modules on $(\mathit{Sch}/S)_\tau$ is denoted $\textit{Adeq}(\mathcal{O})$ or $\textit{Adeq}((\mathit{Sch}/S)_\tau , \mathcal{O})$. If we want to think just about the abelian category of adequate modules without choosing a topology we simply write $\textit{Adeq}(S)$.

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