Abstract
We study the properties of torsion pairs in triangulated category by introducing the notions of d-Ext-projectivity and d-Ext-injectivity. In terms of -mutation of torsion pairs, we investigate the properties of torsion pairs in triangulated category under some conditions on subcategories and in .
Highlights
The notion of torsion theory in abelian categories was introduced by Dickson in 1966
We study the properties of torsion pairs in triangulated category C by introducing the notions of d-Ext-projectivity and d-Ext-injectivity
In terms of D -mutation of torsion pairs, we investigate the properties of torsion pairs in triangulated category U Z D under some conditions on subcategories Z and D in C
Summary
The notion of torsion theory (torsion pairs) in abelian categories was introduced by Dickson in 1966. Torsion theory plays an important role in the investigation of an abelian category. An abelian category is naturally embedded in a triangulated category like the bounded derived category. The analogous definition of torsion pairs in triangulated category is closely related to the notion of a t-structure. Bernstein and Deligne [1] introduce the definition of a t-structure in a triangulated cate-
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