Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 8.6.6.4. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then the evaluation functor $\operatorname{ev}_{1}: \operatorname{Fun}(\Delta ^1,\operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{C}}$ is a cocartesian fibration, which is cocartesian dual to the projection map $\lambda _{+}: \operatorname{Tw}(\operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{C}}$ of Notation 8.1.1.6. This follows by combining Proposition 8.6.6.1 with Corollary 8.6.3.18 (applied to the opposite $\infty $-category $\operatorname{\mathcal{C}}^{\operatorname{op}}$).