Wide Subcategories and Lattices of Torsion Classes

Sota Asai*, Calvin Pfeifer

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this paper, we study the relationship between wide subcategories and torsion classes of an abelian length category A from the point of view of lattice theory. Motivated by τ-tilting reduction of Jasso, we mainly focus on intervals [U, T] in the lattice torsA of torsion classes in A such that W: = U∩ T is a wide subcategory of A; we call these intervals wide intervals. We prove that a wide interval [U, T] is isomorphic to the lattice torsW of torsion classes in the abelian category W. We also characterize wide intervals in two ways: First, in purely lattice theoretic terms based on the brick labeling established by Demonet–Iyama–Reading–Reiten–Thomas; and second, in terms of the Ingalls–Thomas correspondences between torsion classes and wide subcategories, which were further developed by Marks–Šťovíček.

Original languageEnglish
JournalAlgebras and Representation Theory
ISSN1386-923X
DOIs
Publication statusE-pub ahead of print - 5. Sep 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.

Keywords

  • Lattice theory
  • Torsion pairs
  • Wide subcategories

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