Proof.
Part ([00KP]) is straightforward. Thereafter, for part ([00KQ]) it suffices to show that \(\mathcal R= S^\bot\) (so that \((\mathcal L,\mathcal R)\) is indeed the factorization system generated by \(S\) via proposition B.1.14). The containment \(\mathcal R\subseteq S^\bot\) follows from the fact that the Cartesian monodromy functors preserve the right classes, while the containment \(\mathcal R\supseteq S^\bot\) follows from the explicit description of \(\mathcal R\). ◻