Kerodon

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Proposition 9.5.4.3 (Presentability of Diagram $\infty $-Categories). Let $\operatorname{\mathcal{C}}$ be a presentable $\infty $-category and let $K$ be a small simplicial set. Then the diagram $\infty $-category $\operatorname{Fun}(K, \operatorname{\mathcal{C}})$ is presentable.

Proof. It follows from Proposition 9.4.8.1 that $\operatorname{Fun}(K, \operatorname{\mathcal{C}})$ is accessible and from Proposition 7.1.8.2 that it is cocomplete. $\square$