As a general framework for the studies of t-structures on triangulated categories and torsion
pairs in abelian categories, we introduce the notions of extriangulated categories with …

We generalize the “facial weak order” of a finite Coxeter group to a partial order on a set of
intervals in a complete lattice. We apply our construction to the lattice of torsion classes of a …

We introduce image-cokernel-extension-closed (ICE-closed) subcategories of module
categories. This class unifies both torsion classes and wide subcategories. We show that …

We establish some properties of $\tau $-exceptional sequences for finite-dimensional
algebras. In an earlier paper, we established a bijection between the set of ordered support …

As a general framework for the studies of $ t $-structures on triangulated categories and
torsion pairs in abelian categories, we introduce the notions of extriangulated categories …

We study IE-closed subcategories of a module category, subcategories which are closed
under taking Images and Extensions. We investigate the relation between IE-closed …

The pop-stack operator of a finite lattice $ L $ is the map $\mathrm {pop}^{\downarrow}
_L\colon L\to L $ that sends each element $ x\in L $ to the meet of $\{x\}\cup\text {cov} _L (x) …

In a triangulated category equipped with a $ t $-structure, we investigate a relation between
ICE-closed (= Image-Cokernel-Extension-closed) subcategories of the heart of the $ t …

From support 𝜏-tilting posets to algebras I Page 1 TRANSACTIONS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 377, Number 5, May 2024, Pages 3749–3766 https://doi.org/10.1090/tran/9137 …

Intervals and hearts of intervals in the lattice of torsion parts for an abelian category are
closely related to various concepts such as wide subcategory, ICE-closed subcategory, and …