Remark 6.3.3.5. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a reflective localization of $\infty $-categories. Then there exists a functor $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$ and a natural transformation $\eta : \operatorname{id}_{\operatorname{\mathcal{C}}} \rightarrow G \circ F$ which is the unit of an adjunction between $F$ and $G$. The natural transformation $\eta $ is generally not an isomorphism (unless $F$ is an equivalence of $\infty $-categories). However, our assumption that $F$ is a reflective localization guarantees that there exists a natural isomorphism $\epsilon : F \circ G \xrightarrow {\sim } \operatorname{id}_{\operatorname{\mathcal{D}}}$ which is compatible with $\eta $ up to homotopy. In particular, for every object $X \in \operatorname{\mathcal{C}}$, the composition
is homotopic to the identity $\operatorname{id}_{ F(X) }$, which guarantees that $F( \eta _ X )$ is an isomorphism in $\operatorname{\mathcal{D}}$.