Abstract
Let ๐ be a triangulated category. When ฯ is a functorially finite subcategory of ๐, Jรธtrgensen showed that the stable category ๐/ฯ is a pretriangulated category. A pair (๐ณ, ๐ด) of subcategories of ๐ with ฯ โ ๐ณ โฉ ๐ด gives rise to a pair (๐ณ/ฯ, ๐ด/ฯ) of subcategories of ๐/ฯ. In this article, we find conditions for (๐ณ/ฯ, ๐ด/ฯ) to be a torsion pair in terms of properties of the pair (๐ณ, ๐ด). In particular, we obtain necessary and sufficient conditions for (๐ณ/ฯ, ๐ด/ฯ) to be a torsion pair in the stable category ๐/ฯ when ฯฯ = ฯ, where ฯ is the AuslanderโReiten translation.
ACKNOWLEDGMENTS
The authors sincerely thank the referee for the very helpful comments and suggestions.
Notes
Communicated by A. Facchini.