From recollement of triangulated categories to recollement of abelian categories
The goal of the paper is to show that if a triangulated category \(\mathcal D\) admits a recollement with respect to the triangulated categories \(\mathcal D'\), \(\mathcal D''\) given by the maps \(i_*:\mathcal D'\to \mathcal D\), \(j^ *:\mathcal D\to \mathcal D''\), \(i^ *,i^ !:\mathcal D\to \mathcal D'\) and \(j_!,j_*:\mathcal D''\to \mathcal D\), then the induced abelian category \(\mathcal D/\mathcal T\) (where \(\mathcal T\) is a cluster tilting subcategory of \(\mathcal D\)) also admits a recollement relative to the abelian categories \(\mathcal D'/i^ *(\mathcal T)\) and \(\mathcal D''/j^ *(\mathcal T)\), provided that \(\mathcal T\) satisfies \(i_*i^ *(\mathcal T)\subset \mathcal T\), \(j_*j^*(\mathcal T)\subset \mathcal T\).
scientific article; zbMATH DE number 5723660
scientific article