In this paper we continue the project of generalizing tilting theory to the category of
contravariant functors $ Mod (C) $, from a skeletally small preadditive category $ C $ to the …

The notion of quotient and localization of abelian categories by dense subcategories (ie,
Serre classes) was introduced by Gabriel, and plays an important role in ring theory [6, 131 …

An algebra is said to be-tilting finite provided it has only a finite number of-rigid objects up to
isomorphism. To each such algebra, we associate a category whose objects are the wide …

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 …

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 B be an extriangulated category with enough projectives and enough injectives. Let C be
a fully rigid subcategory of B which admits a twin cotorsion pair ((C, K),(K, D)). The quotient …

In the setting of compactly generated triangulated categories, we show that the heart of a
(co) silting t-structure is a Grothendieck category if and only if the (co) silting object satisfies …

The trivial extensions of a quasi-abelian category by means of a fully exact endofunctor are
again quasi-abelian. Using the one-to-one correspondence between quasi-abelian …

In this article, we prove that if (A, B, C) is a recollement of extriangulated categories, then
torsion pairs in A and C can induce torsion pairs in B, and the converse holds under natural …

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 …