Kerodon

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

Example 5.3.4.4. Let $\operatorname{\mathcal{E}}$ be an $\infty $-category equipped with cocartesian fibration $U: \operatorname{\mathcal{E}}\rightarrow \Delta ^1$ having fibers $\operatorname{\mathcal{E}}_0 = \{ 0\} \times _{\Delta ^1} \operatorname{\mathcal{E}}$ and $\operatorname{\mathcal{E}}_{1} = \{ 1\} \times _{ \Delta ^1} \operatorname{\mathcal{E}}$. Choose a functor $F: \operatorname{\mathcal{E}}_0 \rightarrow \operatorname{\mathcal{E}}_1$ and a morphism $h: \Delta ^1 \times \operatorname{\mathcal{E}}_0 \rightarrow \operatorname{\mathcal{E}}$ which witnesses $F$ as given by covariant transport along the nondegenerate edge of $\Delta ^1$, in the sense of Definition 5.2.2.4. Then $F$ can be identified with a diagram $\mathscr {F}: [1] \rightarrow \operatorname{QCat}$, and the map

\[ \underset { \longrightarrow }{\mathrm{holim}}(\mathscr {F}) = ( \Delta ^1 \times \operatorname{\mathcal{E}}_0 ) \coprod _{ ( \{ 1\} \times \operatorname{\mathcal{E}}_0)} \operatorname{\mathcal{E}}_1 \xrightarrow {(h,\operatorname{id})} \operatorname{\mathcal{E}} \]

is a scaffold.