Kerodon

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$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 8.4.2.6. Let $\operatorname{\mathcal{C}}$ be a locally small category. Then the evaluation profunctor

\[ \operatorname{ev}: \operatorname{\mathcal{C}}^{\operatorname{op}} \times \operatorname{Fun}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}}) \rightarrow \operatorname{\mathcal{S}}\quad \quad (X, \mathscr {F}) \mapsto \mathscr {F}(X) \]

is corepresentable by the covariant Yoneda embedding $h_{\bullet }: \operatorname{\mathcal{C}}\rightarrow \operatorname{Fun}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}})$.