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Applications of balanced pairs

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    HuanHuan Li, JunFu Wang & ZhaoYong Huang

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  1. HuanHuan Li
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  2. JunFu Wang
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  3. ZhaoYong Huang
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Correspondence to ZhaoYong Huang.

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Li, H., Wang, J. & Huang, Z. Applications of balanced pairs. Sci. China Math. 59, 861–874 (2016). https://doi.org/10.1007/s11425-015-5094-1

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  • DOI: https://doi.org/10.1007/s11425-015-5094-1

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