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 …

We study triangulated categories and torsion theories in them, and compare two definitions
of torsion theories in this work. The most important types of torsion theories—weight …

For an abelian length category $\mathcal {A} $ with only finitely many isoclasses of simple
objects, we have the wall-chamber structure and the TF equivalence in the dual real …

We investigate the structure of certain almost split sequences in $\mathcal {P}(\Lambda) $,
ie, the category of morphisms between projective modules over an Artin algebra $\Lambda …

We prove that the Drinfeld center $ Z (\mathcal {C}) $ of a pivotal finite tensor category
$\mathcal {C} $ comes with the structure of a ribbon Grothendieck-Verdier category in the …

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 …

For a ring Λ with a Krull-Schmidt homotopy category, we study mutation theory on 2-term
silting complexes. As a consequence, mutation works when Λ is a complete noetherian …

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 …

Hearts of cotorsion pairs on extriangulated categories are abelian categories. On the other
hand, hearts of twin cotorsion pairs are not always abelian. They were shown to be semi …

Given a tensor category C, one constructs its Drinfeld center Z (C) which is a braided tensor
category, having as objects pairs (X, lambda), where X in Obj (C) and lambda is a half …