Let $\Lambda $ be a finite-dimensional algebra. A wide subcategory of $\mathsf
{mod}\Lambda $ is called left finite if the smallest torsion class containing it is functorially …

For a finite‐dimensional algebra A, we establish correspondences between torsion classes
and wide subcategories in mod (A). In case A is representation finite, we obtain an explicit …

Let $\mathcal {A} $ be an abelian length category containing a $ d $-cluster tilting
subcategory $\mathcal {M} $. We prove that a subcategory of $\mathcal {M} $ is a $ d …

Let Φ be a finite dimensional algebra over an algebraically closed field k and assume gldim
Φ≤ d, for some fixed positive integer d. For d= 1, Brüning proved that there is a bijection …

The class of support-tilting modules was introduced recently by Adachi et al. These modules
complete the class of tilting modules from the point of view of mutations. Given a finite …

Abstract Let E=(A, S) be an exact category with enough projectives P. We introduce the
notion of support τ-tilting subcategories of E. It is compatible with the existing definitions of …

Let $\mathcal {A} $ be a Hom-finite abelian category with enough projectives. In this note,
we show that any covariantly finite $\tau $-rigid subcategory is contained in a support $\tau …

The main theme of this paper is to study $\tau $-tilting subcategories in an abelian category
$\mathscr {A} $ with enough projective objects. We introduce the notion of $\tau $-cotorsion …

Let C be a triangulated category with shift functor [1] and R a rigid subcategory of C. We
introduce the notions of two-term R [1]-rigid subcategories, two-term (weak) R [1]-cluster …

Let R be a ring and P be an (infinite dimensional) partial tilting module. We show that the
perpendicular category of P is equivalent to the full module category Mod-S where S= End …