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Remark Let $\operatorname{\mathcal{C}}$ be a locally small $\infty $-category and let $X$ be an object of $\operatorname{\mathcal{C}}$. In ยง5.6.6, we proved that there exists a functor $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{S}}$ which is corepresented by $X$, and that $\mathscr {F}$ is uniquely determined up to isomorphism (Theorem Proposition can be regarded as a more refined version of this uniqueness assertion: the functor $\mathscr {F}$ is characterized, up to isomorphism, by the requirement that it corepresents the evaluation functor

\[ \operatorname{ev}_{X}: \operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{S}}) \rightarrow \operatorname{\mathcal{S}}\quad \quad \mathscr {G} \mapsto \mathscr {G}(X). \]