Kerodon

Example 8.3.4.3. Let $\operatorname{\mathcal{C}}$ be a locally $\kappa $-small $\infty $-category, and let $\mathscr {F}: \operatorname{\mathcal{C}}^{\operatorname{op}} \rightarrow \operatorname{\mathcal{S}}^{<\kappa }$ be a functor. Then $\mathscr {F}$ is representable by an object $X \in \operatorname{\mathcal{C}}$ (in the sense of Variant 5.6.6.2) if and only if, when regarded as a profunctor from $\Delta ^0$ to $\operatorname{\mathcal{C}}$, it is representable by the functor $\Delta ^0 \rightarrow \{ X\} \hookrightarrow \operatorname{\mathcal{C}}$ (in the sense of Definition 8.3.4.2).