Wide subcategories and lattices of torsion classes

Sota Asai*, Calvin Pfeifer


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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.

TidsskriftAlgebras and Representation Theory
Udgave nummer6
Sider (fra-til)1611-1629
StatusUdgivet - dec. 2022

Bibliografisk note

Funding Information:
The first named author was supported by Japan Society for the Promotion of Science KAKENHI JP16J02249, JP19K14500 and JP20J00088.

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


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