# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Corollary 8.3.2.21. Let $\operatorname{\mathcal{C}}$ be a locally small $\infty$-category, and let $\operatorname{Fun}^{\mathrm{corep}}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{S}})$ denote the full subcategory of $\operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{S}})$ spanned by the corepresentable functors. Then the evaluation map

$\operatorname{ev}: \operatorname{Fun}^{\mathrm{corep}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{S}}) \times \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{S}}\quad \quad (F,C) \mapsto F(C)$

is a balanced profunctor.