Recollements of extriangulated categories

Li Wang, Jiaqun Wei, Haicheng Zhang Colloquium Mathematicum MSC: 18E05, 18E10. DOI: 10.4064/cm8457-2-2021 Published online: 31 May 2021

Abstract

We give a simultaneous generalization of recollements of abelian categories and triangulated categories, which we call recollements of extriangulated categories. For a recollement $(\mathcal {A}$, $\mathcal {B}$, $\mathcal {C})$ of extriangulated categories, we show that cotorsion pairs in $\mathcal {A}$ and $\mathcal {C}$ induce cotorsion pairs in $\mathcal {B}$ under certain conditions. As an application, our main result recovers a result given by Chen for recollements of triangulated categories, and it also shows a new phenomenon when it is applied to abelian categories.

Authors

  • Li WangInstitute of Mathematics
    School of Mathematical Sciences
    Nanjing Normal University
    Nanjing 210023, P.R. China
    e-mail
  • Jiaqun WeiInstitute of Mathematics
    School of Mathematical Sciences
    Nanjing Normal University
    Nanjing 210023, P.R. China
    e-mail
  • Haicheng ZhangInstitute of Mathematics
    School of Mathematical Sciences
    Nanjing Normal University
    Nanjing 210023, P.R. China
    e-mail

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