Suppose that 
is a reflective localization and that \((\mathcal L,\mathcal R)\) is a factorization system on \(\mathcal C\). Suppose further that \(L(\mathcal L)\) is stable under retracts and that \(RL(\mathcal R) \subseteq \mathcal R\).
The pair \((L(\mathcal L),L(\mathcal R))\) forms a factorization system on \(\mathcal D\), in which the factorization of a morphism \(d \xrightarrow{f} d'\) is given by the lower composite in the commutative diagram
Moreover, considering \(\mathcal D\) as a full subcategory of \(\mathcal C\) (via \(R\)), the right class \(L(\mathcal R)\) is intersected from \(\mathcal R\) (i.e. we have \(RL(\mathcal R) = \mathcal R\cap R(\mathcal D)\)).Suppose further that \(\mathcal C\) and \(\mathcal D\) are presentable and that \((\mathcal L,\mathcal R)\) is generated by a set \(S\) of morphisms in \(\mathcal C\). Then, \((L(\mathcal L),L(\mathcal R))\) is generated by the set \(L(S)\) of morphisms in \(\mathcal D\).
Suppose that \(\mathcal C\) is (symmetric) monoidal compatible with both the reflective localization (recall Subsection A.8.9) and with the factorization system (recall Definition B.1.12). Then, the induced (symmetric) monoidal structure on \(\mathcal D\) is compatible with the factorization system \((L(\mathcal L),L(\mathcal R))\).