Idempotent completion of pretriangulated categories

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• 作者：Jichun Liu (1)
  Longgang Sun (2)
  
• 关键词：idempotent completion ; pretriangulated category ; torsion pair ; 16B50 ; 18E05 ; 18E30 ; 18E40
• 刊名：Czechoslovak Mathematical Journal
• 出版年：2014
• 出版时间：June 2014
• 年：2014
• 卷：64
• 期：2
• 页码：477-494
• 全文大小：205 KB
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• 作者单位：Jichun Liu (1)
  Longgang Sun (2)
  
  1. Department of Mathematics and Physics, Fujian Jiangxia University, No. 2, Xiyuangong Road, Fuzhou, Fujian Province, 350 108, China
  2. School of Mathematical Sciences, University of Science and Technology of China, No 96, Jinzhai Road, Hefei, Anhui Province, 230 026, China
  
• ISSN：1572-9141

文摘

A pretriangulated category is an additive category with left and right triangulations such that these two triangulations are compatible. In this paper, we first show that the idempotent completion of a left triangulated category admits a unique structure of left triangulated category and dually this is true for a right triangulated category. We then prove that the idempotent completion of a pretriangulated category has a natural structure of pretriangulated category. As an application, we show that a torsion pair in a pretriangulated category extends uniquely to a torsion pair in the idempotent completion.