Remark 4.5.2.15. In the situation of Proposition 4.5.2.14, it suffices to verify that the diagram (4.25) is a homotopy pullback square in the case where $X$ is an $\infty $-category. In fact, we will later see that it suffices to consider the case where $X = \Delta ^1$ (Corollary 4.5.7.4).

$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$