Remark 9.5.1.7 (Sizes of Presentable $\infty $-Categories). Let $\operatorname{\mathcal{C}}$ be a presentable $\infty $-category. We then have two possibilities:
The $\infty $-category $\operatorname{\mathcal{C}}$ is equivalent to the nerve of a partially ordered set $Q$. In this case, Example 9.5.1.5 shows that $Q$ is small, so that $\operatorname{\mathcal{C}}$ is essentially small.
The $\infty $-category $\operatorname{\mathcal{C}}$ is not equivalent to the nerve of a partially ordered set. In this case, Proposition 7.1.2.15 shows that $\operatorname{\mathcal{C}}$ cannot be essentially small.