Kerodon

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

Example 5.2.6.13. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category equipped with a functor $\pi : \operatorname{\mathcal{C}}\rightarrow \Delta ^1$ having fibers $\operatorname{\mathcal{C}}(0) = \{ 0\} \times _{\Delta ^1} \operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{C}}(1) = \{ 1\} \times _{ \Delta ^1} \operatorname{\mathcal{C}}$. By virtue of Example 5.2.6.10, choosing a scaffold of $\pi $ is equivalent to choosing a functor $F: \operatorname{\mathcal{C}}(0) \rightarrow \operatorname{\mathcal{C}}(1)$ together with a map $h: \Delta ^1 \times \operatorname{\mathcal{C}}(0) \rightarrow \operatorname{\mathcal{C}}$ which witnesses $F$ as given by covariant transport along the nondegenerate edge of $\Delta ^1$, in the sense of Definition 5.2.2.1.