Kerodon

Example 6.2.2.4. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $\operatorname{\mathcal{C}}' \subseteq \operatorname{\mathcal{C}}$ be a full subcategory, and let $u: X \rightarrow Y$ be a morphism of $\operatorname{\mathcal{C}}$. If $X$ belongs to the subcategory $\operatorname{\mathcal{C}}'$, then $u$ exhibits $Y$ as a $\operatorname{\mathcal{C}}'$-reflection of $X$ if and only if it is an isomorphism. Similarly, if $Y$ belongs to $\operatorname{\mathcal{C}}'$, then $u$ exhibits $X$ as a $\operatorname{\mathcal{C}}'$-coreflection of $Y$ if and only if it is an isomorphism.