PlanetPhysics/Canonical Localizing System

Let $$R$$ be a ring. The canonical localizing system $$S_{cl}$$ on $$R$$ is defined as the strongest localizing system $$F$$ on $$R$$, such that $$R$$ is $$F$$-closed.

Note that there is a localizing subcategory $$\mathcal{F}$$ that contains all strongest localizing systems $$F$$.