# Kerodon

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

Remark 7.4.3.10. In the situation of Proposition 7.4.3.9, suppose that the simplicial sets $\operatorname{\mathcal{E}}$ and $\operatorname{\mathcal{C}}$ are small. Then the localization $\operatorname{\mathcal{E}}[W^{-1}]$ supplied by Proposition 6.3.2.1 can also be chosen to be small. It follows that the simplicial set $\overline{\operatorname{\mathcal{E}}}$ constructed in the proof is also small.