Applications of balanced pairs

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• 作者：HuanHuan Li ; JunFu Wang ; ZhaoYong Huang
• 关键词：balanced pairs ; relative cotorsion pairs ; relative derived categories ; relative singularity categories ; relative (co)resolution dimension
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：59
• 期：5
• 页码：861-874
• 全文大小：237 KB
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• 作者单位：HuanHuan Li (1)
  JunFu Wang (1)
  ZhaoYong Huang (1)
  
  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

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.