Remark 11.4.0.1. The converse of Lemma 6.2.3.11 is true as well: if $\operatorname{\mathcal{E}}'$ is a reflective subcategory of $\operatorname{\mathcal{E}}$, then the collection of $\operatorname{\mathcal{E}}'$-local equivalences satisfies conditions $(1)$ through $(4)$. Condition $(3)$ is tautology, condition $(4)$ is a reformulation of the assumption that $\operatorname{\mathcal{E}}'$ is reflective, and conditions $(1)$ and $(2)$ follow from Remarks 6.2.2.4 and 6.2.2.5, respectively.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$