# Kerodon

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

Remark 4.6.5.7. Let $\operatorname{\mathcal{C}}$ be a simplicial set containing vertices $X$ and $Y$. Then the pinch inclusion maps

$\operatorname{Hom}_{\operatorname{\mathcal{C}}}^{\mathrm{L}}(X,Y) \xrightarrow { \iota ^{\mathrm{L}}_{X,Y} } \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y) \xleftarrow { \iota ^{\mathrm{R}}_{X,Y} } \operatorname{Hom}_{\operatorname{\mathcal{C}}}^{\mathrm{R}}(X,Y)$

are monomorphisms (see Remark 4.6.4.14).