Remark 9.4.6.15. By definition, an inner fibration of simplicial sets $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ is flat if, for every $2$-simplex $\sigma $ of $\operatorname{\mathcal{C}}$, the inclusion map
\[ \Lambda ^{2}_{1} \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}\hookrightarrow \Delta ^2 \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}} \]
is a categorical equivalence of simplicial sets. It follows from Corollary 9.4.6.14 that it suffices to check this condition in the case where $\sigma $ is nondegenerate.