Reduction of Wide Subcategories and Recollements

Abstract

In this paper, we prove a reduction result on wide subcategories of abelian categories which is similar to the Calabi-Yau reduction, silting reduction and [Formula: see text]-tilting reduction. More precisely, if an abelian category [Formula: see text] admits a recollement relative to abelian categories [Formula: see text] and [Formula: see text], which is denoted by [Formula: see text], then the assignment [Formula: see text] defines a bijection between wide subcategories in [Formula: see text] containing [Formula: see text] and wide subcategories in [Formula: see text]. Moreover, a wide subcategory [Formula: see text] of [Formula: see text] containing [Formula: see text] admits a new recollement relative to [Formula: see text] and [Formula: see text] which is induced from the original recollement.