# Kerodon

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Example 7.1.5.9. Let $U: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an inner fibration of $\infty$-categories. Then:

• A morphism $e$ of $\operatorname{\mathcal{C}}$ is $U$-cartesian (in the sense of Definition 5.1.1.1) if and only if it is a $U$-limit diagram when viewed as a morphism of simplicial sets $(\Delta ^0)^{\triangleleft } \rightarrow \operatorname{\mathcal{C}}$.

• A morphism $f$ of $\operatorname{\mathcal{C}}$ is $U$-cocartesian (in the sense of Definition 5.1.1.1) if and only if it is a $U$-colimit diagram when viewed as a morphism of simplicial sets $(\Delta ^0)^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$.

This follows by combining Remark 7.1.5.8 with Proposition 5.1.1.13.