Kerodon

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

Remark 5.2.6.4. Let $\overrightarrow {X}$ be a diagram of simplicial sets

\[ X(0) \xrightarrow {F(1)} X(1) \xrightarrow { F(2) } X(2) \xrightarrow {F(3)} \cdots \xrightarrow {F(n)} X(n). \]

By construction, the mapping simplex $M(\overrightarrow {X})$ is equipped with a projection map $M(\overrightarrow {X}) \rightarrow \Delta ^ n$. Moreover, for each integer $0 \leq i \leq n$, the fiber $\{ i\} \times _{\Delta ^ n} M( \overrightarrow {X} )$ is canonically isomorphic to the simplicial set $X(i)$ (Remark 5.2.6.2).