Kerodon

Remark 9.6.9.22. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Any intersection of strongly saturated collections of morphisms of $\operatorname{\mathcal{C}}$ is also strongly saturated. In particular, for any collection $W$ of morphisms of $\operatorname{\mathcal{C}}$, there is a smallest collection $\overline{W}$ which is strongly saturated and contains $W$. We will refer to $\overline{W}$ as the strongly saturated collection generated by $W$. We will say that a collection of morphisms is accessibly strongly saturated if it has the form $\overline{W}$, where $W$ is a small collection of morphisms of $\operatorname{\mathcal{C}}$.