In a compactly generated triangulated category, we introduce a class of tilting objects
satisfying a certain purity condition. We call these the decent tilting objects and show that the …

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 …

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 …

Tilting modules play an important role in the representation theory of finite dimensional
algebras. Traditionally, one considers tilting modules of projective dimension at most one …

Tilting modules appear in a variety of ways: their first definition was in the context of finite
dimensional algebras over a field. Later, they appeared naturally in applications of the …

We prove a generalization to the context of topological tilting modules of the fact that a tilting
module is faithfully balanced and also a tilting module over its endomorphism ring. Some …

Let $ T $ be a $1 $-tilting module whose tilting torsion pair $({\mathcal T},{\mathcal F}) $ has
the property that the heart ${\mathcal H} _t $ of the induced $ t $-structure (in the derived …

Let T be an infinitely generated tilting module of projective dimension at most one over an
arbitrary associative ring A, and let B be the endomorphism ring of T. We prove that if T is …

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in
any triangulated category D with arbitrary (set-indexed) coproducts. We show that …

We show that a right triangulated category is best behaved when its shift satisfies conditions
making it what we call a right semi-equivalence. We consider right triangulated categories …