For four wide classes of topological rings R, we show that all flat left R-contramodules have
projective covers if and only if all flat left R-contramodules are projective if and only if all left …

We introduce the notion of big tilting complexes over associative rings, which is a
simultaneous generalization of good tilting modules and tilting complexes over rings. Given …

We introduce symmetric subcategories of abelian categories and show that the derived
category of the endomorphism ring of any good tilting module over a ring is a recollement of …

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 …

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 …

Given a torsion pair t=(T, F) in a module category R-Mod we give necessary and sufficient
conditions for the associated Happel–Reiten–Smalø t-structure in D (R) to have a heart Ht …

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 …

Given two ringsRandS, we study the category equivalences T⇄ Y, where T is a torsion class
ofR-modules and Y is a torsion-free class ofS-modules. These equivalences correspond to …

In [R. Colpi, KR Fuller, Tilting objects in abelian categories and quasitilted rings, Trans.
Amer. Math. Soc., in press] tilting objects in an arbitrary abelian category H are introduced …

Let X be a semibrick in an extriangulated category C. Let T be the filtration subcategory
generated by X. We give a one-to-one correspondence between simple semibricks and …