Left Schur subcategories in recollements

Abstract

Recently left Schur subcategories in a length abelian category were introduced by Enomoto, which unify torsion-free classes and wide subcategories. In this paper, we give a construction of left Schur subcategories in the recollements of length abelian categories. Moreover, we show that the construction restricts to wide subcategories and torsion-free classes. As a consequence, we obtain an explicit construction of cofinally closed monobricks in recollements. Finally, we apply the results to a special case of the MacPherson-Vilonen construction of abelian recollements and triangular matrix algebras.

Comments welcome