Example 7.1.6.10. Let $K$ be a weakly contractible simplicial set and let $U: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a right fibration of $\infty $-categories. Then every morphism $\overline{f}: K^{\triangleleft } \rightarrow \operatorname{\mathcal{C}}$ is a $U$-limit diagram (see Proposition 4.3.7.6). Similarly, if $U$ is a left fibration, then every morphism $\overline{g}: K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$ is a $U$-colimit diagram.
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