t-Structures are Normal Torsion Theories

摘要

We characterize t-structures in stable a-categories as suitable quasicategorical factorization systems. More precisely we show that a t-structure oe"+/- on a stable a-category C is equivalent to a normal torsion theory oe"1/2 on C, i.e. to a factorization system oe"1/2 = (oe"", a"(3)) where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.