Warning 9.1.4.11. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be filtered $\infty $-categories. In general, a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ which is weakly right cofinal need not be right cofinal (Exercise 9.1.4.12). That is, the coslice construction appearing in the formulation of Theorem 9.1.4.5 cannot be omitted.
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