# Kerodon

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Example 4.3.5.16. Let $X$ be a simplicial set containing a vertex $x$. Let $Y$ be a simplicial set, and let $v$ and $v'$ denote the cone points of $Y^{\triangleleft }$ and $Y^{\triangleright }$, respectively. Then Proposition 4.3.5.13 supplies bijections

$\operatorname{Hom}_{\operatorname{Set_{\Delta }}}( Y, X_{x/} ) \simeq \{ \textnormal{Morphisms f: Y^{\triangleleft } \rightarrow X with f(v) = x} \}$
$\operatorname{Hom}_{\operatorname{Set_{\Delta }}}( Y, X_{/x} ) \simeq \{ \textnormal{Morphisms f: Y^{\triangleright } \rightarrow X with f(v') = x} \} .$