Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 5, pp 1353–1366 | Cite as

Applications of Cotorsion Pairs on Triangulated Categories

  • Haixia ChengEmail author
  • Xiaosheng Zhu
Original Paper


Giving a cotorsion pair in an abelian category \({\mathscr {C}}\), we have a sequence of exact functors between triangulated categories with respect to the pair, and construct right (left) adjoints of the exact functors such that the sequence is a (co)localization sequence. Further, for some especial cotorsion pairs, we gain a recollement and triangle-equivalences between corresponding triangulated categories. In particular, let (\({\mathcal {A}}, {\mathcal {Z}}, {\mathcal {B}}\)) and (\({\mathcal {A}}_{1}, {\mathcal {Z}}_{1}, {\mathcal {B}}_{1}\)) be two complete and hereditary cotorsion triples in \({\mathscr {C}}\) with \({\mathcal {A}}_{1}\subseteq {\mathcal {A}}\). We obtain a triangle-equivalence \(K({\mathcal {A}})\simeq K({\mathcal {B}})\), which restricts to an equivalence \(K({\mathcal {A}}_{1})\simeq K({\mathcal {B}}_{1})\).


Cotorsion pair Localization sequence Relative derived category Gorenstein derive category 

Mathematics Subject Classification

18E30 18E35 55U35 



The authors would like to thank the referee for his/her helpful comments and suggestions. This work was partially supported by the National Natural Science Foundation of China (No. 11301007) and the Key University Science Research Project of Anhui Province (No. KJ2018A0302).


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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsAnhui Normal UniversityWuhuChina
  2. 2.Department of MathematicsNanjing UniversityNanjingChina

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