Kerodon

Example 7.1.6.3. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and $U: \operatorname{\mathcal{C}}\rightarrow \Delta ^{0}$ be the projection map. Then a morphism $\overline{f}: K^{\triangleleft } \rightarrow \operatorname{\mathcal{C}}$ is a $U$-limit diagram (in the sense of Definition 7.1.6.1) if and only if it is a limit diagram (in the sense of Definition 7.1.3.4). Similarly, a morphism $\overline{g}: K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$ is a $U$-colimit diagram if and only if it is a colimit diagram.