Torsion pairs were introduced by Dickson in 1966 as a generalization of the concept of
torsion abelian group to arbitrary abelian categories. Using torsion pairs, we can divide …

In his work [26], SE Dickson defined the notion of torsion theory (now called torsion pair) in
the general framework of abelian categories, which generalizes the concept of …

First, we show that a compact object C in a triangulated category, which satisfies suitable
conditions, induces a t-structure. Second, in an abelian category we show that a complex P …

Aim: A torsion pair in an abelian category is a decomposition of it into two parts: a torsion
and a torsionfree part. It turns out that both the study of individual torsion pairs and the study …

Mutation of compact silting objects is a fundamental operation in the representation theory of
finite-dimensional algebras due to its connections to cluster theory and to the lattice of …

Mutation of compact silting objects is a fundamental operation in the representation theory of
finite-dimensional algebras due to its connections to cluster theory and to the lattice of …

It is a well established fact that the notions of quasi-abelian categories and tilting torsion
pairs are equivalent. This equivalence fits in a wider picture including tilting pairs of t …

Chapter 0 gives a gentle background to the thesis. It begins with some general notions and
concepts from homological algebra. For example, not only are the notions of universal …

Throughout the paper A will denote an artin algebra and mod A will denote the category of
finitely generated A-modules. Recently, subcategories of mod A which are the torsion free …

We generalize basic results about classical tilting modules and partial tilting modules to the
infinite dimensional case, over an arbitrary ring R. The methods employed combine classical …