Definition 9.1.4.1. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. We say that $F$ is weakly right cofinal if, for every object $D \in \operatorname{\mathcal{D}}$, there exists an object $C \in \operatorname{\mathcal{C}}$ and a morphism $v: D \rightarrow F(C)$ in the $\infty $-category $\operatorname{\mathcal{D}}$.
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