PlanetPhysics/Canonical Localizing System

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

Note that there is a localizing subcategory $ℱ$ that contains all strongest localizing systems $F$.