3,449 research outputs found

    Reduction of wide subcategories and recollements

    Full text link
    In this paper, we prove that if an abelian category A\mathcal{A} admits a recollement relative to abelian categories Aβ€²\mathcal{A}' and Aβ€²β€²\mathcal{A}'', there is a bijection between wide subcategories in A\mathcal{A} containing iβˆ—(Aβ€²)i_{*}(\mathcal{A}') and wide subcategories in Aβ€²β€²\mathcal{A}'' similar to silting reduction and Ο„\tau-tilting reduction. Moreover, the wide subcategory C\mathcal{C} of A\mathcal{A} containing iβˆ—(Aβ€²)i_{*}(\mathcal{A}') admits a new recollement relative to wide subcategories Aβ€²\mathcal{A}' and jβˆ—(C)j^{*}(\mathcal{C}) which induced from the original recollement.Comment: 9 pages,correct some mistakes and title changed,comments welcom
    • …
    corecore