# Kerodon

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Definition 9.5.0.37. Let $\operatorname{\mathcal{QC}}$ denote the $\infty$-category of small $\infty$-categories (Construction 5.6.4.1), and let $\operatorname{\mathcal{Q}}\subseteq \operatorname{\mathcal{QC}}$ be a full subcategory. We will say that a cocartesian fibration $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ is $\operatorname{\mathcal{Q}}$-small if, for every object $C \in \operatorname{\mathcal{D}}$, the fiber $\operatorname{\mathcal{E}}_{C} = \{ C \} \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}$ is equivalent to an $\infty$-category which belongs to $\operatorname{\mathcal{Q}}$.