Kerodon

Warning 5.4.6.12. Let $\operatorname{\mathcal{C}}$ be an $(\infty ,2)$-category and let $\sigma : \Delta ^{4} \rightarrow \operatorname{\mathcal{C}}$ be a $4$-simplex of $\operatorname{\mathcal{C}}$. For $0 \leq i < j < k \leq 4$, let $\sigma _{kji}$ denote the restriction $\sigma |_{ \operatorname{N}_{\bullet }( \{ i < j < k \} ) }$. Proposition 5.4.6.11 asserts that, if the $2$-simplices $\sigma _{310}$, $\sigma _{420}$, $\sigma _{321}$, and $\sigma _{432}$ are thin, then $\sigma _{430}$ is also thin. Beware that the remaining $2$-simplices $\sigma _{210}$, $\sigma _{410}$, $\sigma _{320}$, $\sigma _{421}$, and $\sigma _{431}$ need not be thin.