Kerodon

Example 7.2.3.8. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. If $\operatorname{\mathcal{C}}_0 \subseteq \operatorname{\mathcal{C}}$ is a reflective subcategory (Definition 6.2.2.1), then the inclusion map $\iota : \operatorname{\mathcal{C}}_0 \hookrightarrow \operatorname{\mathcal{C}}$ is right cofinal (this is a special case of Corollary 7.2.3.7, since Proposition 6.2.2.11 guarantees that $\iota $ has a left adjoint). Similarly, if $\operatorname{\mathcal{C}}_0$ is a coreflective subcategory of $\operatorname{\mathcal{C}}$, then the inclusion $\iota $ is left cofinal.