Kerodon

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

Remark 5.5.3.3. Let $\operatorname{\mathcal{C}}$ be a simplicial set. Then axioms $(3)$ and $(4)$ of Definition 5.5.1.3 can be stated as follows:

$(3')$

Let $X$ be any vertex of $\operatorname{\mathcal{C}}$ and let $q: \operatorname{\mathcal{C}}_{/X} \rightarrow \operatorname{\mathcal{C}}$ be the projection map. Then every degenerate edge of $\operatorname{\mathcal{C}}_{/X}$ is $q$-cocartesian.

$(4')$

Let $X$ be any vertex of $\operatorname{\mathcal{C}}$ and let $q': \operatorname{\mathcal{C}}_{X/} \rightarrow \operatorname{\mathcal{C}}$ be the projection map. Then every degenerate edge of $\operatorname{\mathcal{C}}_{X/}$ is $q'$-cartesian.

Note that $(3')$ and $(4')$ appear as special cases of the conclusion of Proposition 5.5.3.1.