Corollary 9.4.8.11. Suppose we are given a categorical pullback square of $\infty $-categories
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{C}}_{\pm } \ar [r]^-{G_{+}} \ar [d]^{G_{-}} & \operatorname{\mathcal{C}}_{+} \ar [d]^{ F_{+} } \\ \operatorname{\mathcal{C}}_{-} \ar [r]^-{ F_{-} } & \operatorname{\mathcal{C}}. } \]
Assume that $\operatorname{\mathcal{C}}_{-}$, $\operatorname{\mathcal{C}}_{+}$, and $\operatorname{\mathcal{C}}$ are accessible $\infty $-categories and that $F_{-}$ and $F_{+}$ are accessible functors. Then the $\infty $-category $\operatorname{\mathcal{C}}_{\pm }$ and the functors $G_{-}$ and $G_{+}$ are also accessible. Moreover, if $\operatorname{\mathcal{D}}$ is another accessible $\infty $-category, then a functor $T: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}_{\pm }$ is accessible if and only if the compositions $G_{-} \circ T$ and $G_{+} \circ T$ are accessible.