Kerodon

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

Notation 5.1.1.5. Let $q: X \rightarrow S$ be a left fibration of simplicial sets, and let $e: s \rightarrow s'$ be an edge of the simplicial set $S$. We will often use the symbol $e_{!}$ to denote a morphism of Kan complexes $X_{s} \rightarrow X_{s'}$ which is given by covariant transport along $e$. By virtue of Proposition 5.1.1.4, such a morphism exists and is uniquely determined up to homotopy.