Remark 9.2.3.10. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing a $2$-simplex
\[ \xymatrix@C =50pt@R=50pt{ & Y \ar [dr]^{v} & \\ X \ar [ur]^{u} \ar [rr]^{w} & & Z. } \]
If an object $C \in \operatorname{\mathcal{C}}$ is weakly $u$-local and weakly $v$-local, then it is weakly $w$-local. Conversely, if $C$ is weakly $w$-local, then it is weakly $u$-local.