Aran Tattar
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View article: The Structure of Aisles and Co-aisles of t-Structures and Co-t-structures
The Structure of Aisles and Co-aisles of t-Structures and Co-t-structures Open
Right triangulated categories can be thought of as triangulated categories whose shift functor is not an equivalence. We give intrinsic characterisations of when such categories are appearing as the (co-)aisle of a (co-)t-structure in an a…
View article: Stability spaces of string and band modules
Stability spaces of string and band modules Open
The stability space of a module is the cone of vectors which make the module semistable. These cones are defined in terms of inequalities; in this paper we draw insights from considering the dual description in terms of non-negative linear…
View article: Weak stability conditions and the space of chains of torsion classes
Weak stability conditions and the space of chains of torsion classes Open
In this paper we show an explicit relation between chains of torsion classes and weak stability conditions over an abelian category. In particular, up to a natural equivalence, they coincide. We investigate topological properties of the sp…
View article: A geometric perspective on the $τ$-cluster morphism category
A geometric perspective on the $τ$-cluster morphism category Open
We show how the $τ$-cluster morphism category may be defined in terms of the wall-and-chamber structure of an algebra. This geometric perspective leads to a simplified proof that the category is well-defined.
View article: Stability spaces of string and band modules
Stability spaces of string and band modules Open
The stability space of a module is the cone of vectors which make the module semistable. These cones are defined in terms of inequalities; in this paper we draw insights from considering the dual description in terms of non-negative linear…
View article: Stratifying systems and Jordan-Hölder extriangulated categories
Stratifying systems and Jordan-Hölder extriangulated categories Open
Stratifying systems, which have been defined for module, triangulated and exact categories previously, were developed to produce examples of standardly stratified algebras. A stratifying system $Φ$ is a finite set of objects satisfying som…
View article: Right triangulated categories: As extriangulated categories, aisles and\n co-aisles
Right triangulated categories: As extriangulated categories, aisles and\n co-aisles Open
Right triangulated categories can be thought of as triangulated categories\nwhose shift functor is not an equivalence. We give intrinsic characterisations\nof when such categories have a natural extriangulated structure and are\nappearing …
View article: Right triangulated categories: As extriangulated categories, aisles and co-aisles
Right triangulated categories: As extriangulated categories, aisles and co-aisles Open
Right triangulated categories can be thought of as triangulated categories whose shift functor is not an equivalence. We give intrinsic characterisations of when such categories have a natural extriangulated structure and are appearing as …
View article: Intersections, sums, and the Jordan-Hölder property for exact categories
Intersections, sums, and the Jordan-Hölder property for exact categories Open
View article: Intersections, sums, and the Jordan-H\"older property for exact categories
Intersections, sums, and the Jordan-H\"older property for exact categories Open
We investigate how the concepts of intersection and sums of subobjects carry to exact categories. We obtain a new characterisation of quasi-abelian categories in terms of admitting admissible intersections in the sense of Hassoun and Roy. …