Recollements and <i>n</i> -cluster tilting subcategories (Q6594903)

In this paper, the authors explore the intricate relations between three \(n\)-cluster tilting subcategories in a recollement of triangulated categories. Consider a recollement \((\mathcal D',\mathcal D,\mathcal D'')\) of triangulated categories.They demonstrate how an \(n\)-cluster tilting subcategory of can be constructed by gluing together \(n\)-cluster tilting subcategories of \(\mathcal D'\) and \(\mathcal D''\) under specific conditions. Conversely, they establish that an \(n\)-cluster tilting subcategory of \(\mathcal D\) induces corresponding \(n\)-cluster tilting subcategories in \(\mathcal D'\) and \(\mathcal D''\). These results lead to a one-to-one correspondence between certain \(n\)-cluster tilting subcategories of \(\mathcal D\) and pairs of such subcategories in \(\mathcal D'\) and \(\mathcal D''\). Additionally, they derive a recollement of abelian categories from this recollement of triangulated categories, revealing deeper structural connections.