Remark 7.7.1.3. Let $\mathscr {F}, \mathscr {G}: K \rightarrow \operatorname{\mathcal{C}}$ be as in Definition 7.7.1.1, and let $e$ be an edge of the simplicial set $K$. If $\mathscr {F}(e)$ and $\mathscr {G}(e)$ are both isomorphisms in the $\infty $-category $\operatorname{\mathcal{C}}$, then the diagram (7.79) is automatically a pullback square (see Corollary 7.6.2.27). In particular, to verify that a natural transformation $\gamma : \mathscr {F} \rightarrow \mathscr {G}$ is cartesian, it suffices to check that (7.79) is a pullback square when $e$ is a nondegenerate edge of $K$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$