Kerodon

Remark 9.4.8.2. In the situation of Proposition 9.4.8.1, suppose we are given another accessible $\infty $-category $\operatorname{\mathcal{D}}$ and a functor $T: \operatorname{\mathcal{D}}\rightarrow \operatorname{Fun}(K, \operatorname{\mathcal{C}})$. Then $T$ is accessible if and only if, for every vertex $x \in K$, the composition $\operatorname{\mathcal{D}}\xrightarrow {T} \operatorname{Fun}(K, \operatorname{\mathcal{C}}) \xrightarrow { \operatorname{ev}_{x} } \operatorname{Fun}( \{ x\} , \operatorname{\mathcal{C}}) \simeq \operatorname{\mathcal{C}}$ is an accessible functor. See Proposition 7.1.8.2.