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 be an extriangulated category with enough projectives P \mathcalP and enough
injectives I \mathcalI, and let be a contravariantly finite rigid subcategory of which contains P …

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 …

It is proved that any tilting adjunction is completely described by an exact category with a
coherence property and the closure condition that exact sequences are acyclic. The …

Extriangulated category was introduced by H. Nakaoka and Y. Palu to give a unification of
properties in exact categories and triangulated categories. A notion of tilting (resp., cotilting) …

We define tilting subcategories in arbitrary exact categories to archieve the following. Firstly:
Unify existing definitions of tilting subcategories to arbitrary exact categories. Discuss …

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 …

Let $\mathscr {C} $ be an extriangulated category with enough projectives and injectives.
We give a new definition of tilting subcategories of $\mathscr {C} $ and prove it coincides …

Assume that B is a finite dimensional algebra, and A= B [P 0] is the one-point extension
algebra of B using a finitely generated projective B-module P 0. The categories of B …

An important result in tilting theory states that a class of modules over a ring is a tilting class
if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective …