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 phenomena when it is applied to abelian categories.
Categories: math.RT math.CT math.RA