Proposition 11.9.1.1. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $\operatorname{ev}_{0}, \operatorname{ev}_1: \operatorname{Fun}( \Delta ^1, \operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{C}}$ be the evaluation functors. Let $L$ be the collection of all morphisms $u$ in $\operatorname{Fun}(\Delta ^1, \operatorname{\mathcal{C}})$ such that $\operatorname{ev}_0(u)$ is an isomorphism in $\operatorname{\mathcal{C}}$, and let $R$ be the collection of all morphisms $u$ in $\operatorname{Fun}( \Delta ^1, \operatorname{\mathcal{C}})$ such that $\operatorname{ev}_{1}(u)$ is an isomorphism in $\operatorname{\mathcal{C}}$. Then the maps $\operatorname{Cospan}( \operatorname{ev}_0 )$ and $\operatorname{Cospan}( \operatorname{ev}_1 )$ determine a balanced coupling
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
\[ \lambda : \operatorname{Cospan}^{L,R}( \operatorname{Fun}(\Delta ^1, \operatorname{\mathcal{C}}) ) \rightarrow \operatorname{Fun}^{ \mathrm{iso}, \mathrm{all} }( \operatorname{\mathcal{C}}) \times \operatorname{Fun}^{ \mathrm{all}, \mathrm{iso} }( \operatorname{\mathcal{C}}). \]