Author： Zhou Panyue Xu Jinde Ouyang Baiyu
Publisher： Taylor & Francis Ltd
E-ISSN： 1532-4125|43|8|3498-3514
ISSN： 0092-7872
Source： Communications in Algebra, Vol.43, Iss.8, 2015-08, pp. : 3498-3514
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Abstract
Let be a triangulated category. When ω is a functorially finite subcategory of , Jøtrgensen showed that the stable category /ω is a pretriangulated category. A pair (, ) of subcategories of with ω ⊆ ∩ gives rise to a pair (/ω, /ω) of subcategories of /ω. In this article, we find conditions for (/ω, /ω) to be a torsion pair in terms of properties of the pair (, ). In particular, we obtain necessary and sufficient conditions for (/ω, /ω) to be a torsion pair in the stable category /ω when τω = ω, where τ is the Auslander–Reiten translation.
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