Construction 8.6.3.15. Let $e$ denote the nondegenerate edge of $\Delta ^1$, viewed as an object of the $\infty $-category $\operatorname{Tw}(\Delta ^1)$. For every simplicial set $\operatorname{\mathcal{C}}$, we let
\[ \Xi : \operatorname{Fun}( \Delta ^1, \operatorname{\mathcal{C}}) \rightarrow \operatorname{Cospan}( \operatorname{Tw}(\operatorname{\mathcal{C}}) ) \]
denote the morphism of simplicial sets which corresponds, under the bijection of Proposition 8.1.3.7, to the composite map
\begin{eqnarray*} \operatorname{Tw}( \operatorname{Fun}(\Delta ^1, \operatorname{\mathcal{C}}) ) & \simeq & \{ e \} \times \operatorname{Tw}( \operatorname{Fun}( \Delta ^1, \operatorname{\mathcal{C}}) ) \\ & \hookrightarrow & \operatorname{Tw}(\Delta ^1) \times \operatorname{Tw}( \operatorname{Fun}( \Delta ^1, \operatorname{\mathcal{C}}) ) \\ & \simeq & \operatorname{Tw}( \Delta ^1 \times \operatorname{Fun}( \Delta ^1, \operatorname{\mathcal{C}}) ) \\ & \xrightarrow { \operatorname{Tw}(\operatorname{ev}) } & \operatorname{Tw}( \operatorname{\mathcal{C}}). \end{eqnarray*}