Warning 5.5.6.4. By analogy with Definition 3.2.1.5, it would be natural to refer to the objects $(\operatorname{\mathcal{C}}, C)$ of $\operatorname{\mathcal{QC}}_{\ast }$ as pointed $\infty $-categories. We will avoid using this terminology, since it conflicts with another (related but distinct) notion of pointed $\infty $-category that we will consider later (Definition 
).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$