Remark 9.4.8.10. In the situation of Proposition 9.4.8.9, suppose we are given another accessible $\infty $-category $\operatorname{\mathcal{D}}$ and a functor
\[ T: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}_{\pm } = \operatorname{\mathcal{C}}_{-} \times ^{\mathrm{h}}_{\operatorname{\mathcal{C}}} \operatorname{\mathcal{C}}_{+}. \]
Then $T$ is accessible if and only if the components $T_{-}: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}_{-}$ and $T_{+}: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}_{+}$ are accessible functors (see Corollary 7.1.9.7.