Recollements of extriangulated categories
Volume 167 / 2022
Colloquium Mathematicum 167 (2022), 239-259
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.
