Remark 11.10.3.5. Let $U: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$ be a functor between categories and let $f: X \rightarrow Y$ be a morphism in the category $\operatorname{\mathcal{D}}$. If $f$ is $U$-cartesian, then it is locally $U$-cartesian. If $f$ is $U$-cocartesian, then it is locally $U$-cocartesian. This follows from Remark 11.10.3.4.
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