Science China Mathematics

, Volume 59, Issue 5, pp 861–874 | Cite as

Applications of balanced pairs

  • HuanHuan Li
  • JunFu Wang
  • ZhaoYong Huang


Let (X, Y) be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to (X, Y), and then give some equivalent characterizations when a relative cotorsion pair is hereditary or perfect. We prove that if the X-resolution dimension of Y (resp. Y-coresolution dimension of X) is finite, then the bounded homotopy category of Y (resp. X) is contained in that of X (resp. Y). As a consequence, we get that the right X-singularity category coincides with the left Y-singularity category if the X-resolution dimension of Y and the Y-coresolution dimension of X are finite.


balanced pairs relative cotorsion pairs relative derived categories relative singularity categories relative (co)resolution dimension 


16G25 18G10 18G20 


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© Science China Press and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsNanjing UniversityNanjingChina

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