Example 7.1.5.5. Let $U: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. Then an object $C \in \operatorname{\mathcal{C}}$ is $U$-final if and only if it is a $U$-limit diagram when viewed as a morphism of simplicial sets $(\emptyset )^{\triangleleft } \simeq \Delta ^0 \rightarrow \operatorname{\mathcal{C}}$. Similarly, $C$ is $U$-initial if and only if it is a $U$-colimit diagram when viewed as a morphism of simplicial sets $(\emptyset )^{\triangleright } \simeq \Delta ^0 \rightarrow \operatorname{\mathcal{C}}$.
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