Warning 9.6.8.12. The converse of Corollary 9.6.8.11 is false in general: there are many examples of weak factorization systems which are not factorization systems, even in the setting of ordinary categories. See Example 9.6.0.4 and Exercise 9.6.0.5.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$