# Kerodon

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Example 9.5.0.38. Let $\operatorname{\mathcal{Q}}$ be a full subcategory of $\operatorname{\mathcal{QC}}$, and let $\widetilde{\operatorname{\mathcal{Q}}}$ denote the fiber product $\operatorname{\mathcal{Q}}\times _{ \operatorname{\mathcal{QC}}} \operatorname{\mathcal{QC}}_{\operatorname{Obj}}$: that is, the $\infty$-category of elements of the inclusion map $\operatorname{\mathcal{Q}}\hookrightarrow \operatorname{\mathcal{QC}}$. Then the projection map $V: \widetilde{\operatorname{\mathcal{Q}}} \rightarrow \operatorname{\mathcal{Q}}$ is a $\operatorname{\mathcal{Q}}$-small cocartesian fibration of $\infty$-categories. This follows from Example 5.7.2.18: for every object $Q \in \operatorname{\mathcal{Q}}$, the fiber $\{ Q\} \times _{ \operatorname{\mathcal{Q}}} \widetilde{\operatorname{\mathcal{Q}}}$ is an $\infty$-category equivalent to $Q$.