We revisit a construction of wide subcategories going back to work of Ingalls and Thomas. To a torsion pair in the category R-mod of finitely presented modules over a left artinian ring R, we assign two wide subcategories in the category R - Mod of all R-modules and describe them explicitly in terms of an associated cosilting module. It turns out that these subcategories are coreflective, and we address the question of which wide coreflective subcategories can be obtained in this way. Over a tame hereditary algebra, they are precisely the categories which are perpendicular to collections of pure- injective modules.

Wide coreflective subcategories and torsion pairs

Lidia Angeleri;Francesco Sentieri
2024-01-01

Abstract

We revisit a construction of wide subcategories going back to work of Ingalls and Thomas. To a torsion pair in the category R-mod of finitely presented modules over a left artinian ring R, we assign two wide subcategories in the category R - Mod of all R-modules and describe them explicitly in terms of an associated cosilting module. It turns out that these subcategories are coreflective, and we address the question of which wide coreflective subcategories can be obtained in this way. Over a tame hereditary algebra, they are precisely the categories which are perpendicular to collections of pure- injective modules.
2024
Torsion pair Wide subcategory Silting theory τ-tilting finite algebra Tame hereditary algebra Pure-injective module
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1145112
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