Kerodon

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

Remark 4.4.3.5 (Functoriality). Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. Then $F$ carries the core $\operatorname{\mathcal{C}}^{\simeq }$ into the core $\operatorname{\mathcal{D}}^{\simeq }$ (see Remark 1.4.1.6), and therefore restricts to a morphism of simplicial sets $F^{\simeq }: \operatorname{\mathcal{C}}^{\simeq } \rightarrow \operatorname{\mathcal{D}}^{\simeq }$.