Example 9.5.4.8 (Products of Presentable $\infty $-Categories). Let $\{ \operatorname{\mathcal{C}}_ i \} _{i \in I}$ be a small collection of presentable $\infty $-categories. Then the product $\operatorname{\mathcal{C}}= \prod _{i \in I} \operatorname{\mathcal{C}}_ i$ is presentable. This can be regarded as a special case of Proposition 9.5.4.7 (see Example 7.6.1.20). Alternatively, it follows from Corollary 9.4.6.19 (which guarantees that $\operatorname{\mathcal{C}}$ is accessible) and Example 7.1.3.11 (which guarantees that it is cocomplete).
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