# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Example 6.3.0.7. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor between categories. If $F$ exhibits $\operatorname{\mathcal{D}}$ as a strict localization of $\operatorname{\mathcal{C}}$ with respect to $W$, then $F$ exhibits $\operatorname{\mathcal{D}}$ as a $1$-categorical localization of $\operatorname{\mathcal{C}}$ with respect to $W$ (see Remark 6.3.0.5). The converse is false (except in the trivial case where $\operatorname{\mathcal{C}}$ is empty).