Kerodon

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

Notation 3.2.1.8. Let $(X,x)$ and $(Y,y)$ be pointed simplicial sets. We let $[X, Y]_{\ast }$ denote the set $\pi _{0}( \operatorname{Fun}(X,Y) \times _{ \operatorname{Fun}( \{ x\} , Y) } \{ y\} )$ of pointed homotopy classes of morphisms from $(X,x)$ to $(Y,y)$. If $f: X \rightarrow Y$ is a morphism of pointed simplicial sets, we denote its pointed homotopy class by $[f] \in [X,Y]_{\ast }$.