Related papers: Stability Conditions on Abelian Comma Categories

Let $\mathscr{A}$ be an abelian category and let $\mathscr{C}$ and $\mathscr{D}$ be additive subcategories of $\mathscr{A}$. As a generalization of Gorenstein categories, we introduce one-sided $n$-$(\C,\D)$-Gorenstein categories with…

In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form $n$ over a field $k$ of characteristic not two, and a category arising from an action…

We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…

It is a well-known fact that although the poset of open sets of a topological space is a Heyting algebra, its Heyting implication is not necessarily stable under the inverse image of continuous functions and hence is not a geometric…

A moment category is endowed with a distinguished set of split idempotents, called moments, which can be transported along morphisms. Equivalently, a moment category is a category with an active/inert factorisation system fulfilling two…

2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central to categorical coherence theory. We place a…

This paper studies abelian categories that can be decomposed into smaller abelian categories via iterated recollements - such a decomposition we call a stratification. Examples include the categories of (equivariant) perverse sheaves and…

This paper continues the study of superstability in abstract elementary classes (AECs) satisfying the amalgamation property. In particular, we consider the definition of $\mu$-superstability which is based on the local character…

For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…

We introduce the extension groups between atoms in an abelian category. For a locally noetherian Grothendieck category, the localizing subcategories closed under injective envelopes are characterized in terms of those extension groups. We…

We first study situations where the stable AF-algebras defined by two square primitive nonsingular incidence matrices with nonnegative integer matrix elements are isomorphic even though no powers of the associated automorphisms of the…

We study a class of semistability conditions defined by a system of ample classes for coherent sheaves over a smooth projective variety. Under some necessary boundedness assumptions, we show the existence of a well-behaved chamber structure…

Over any partially ordered abelian group whose positive cone is closed in an appropriate sense and has finitely many faces, modules that satisfy a weak finiteness condition admit finite primary decompositions. This conclusion rests on the…

In a stable abelian group, we characterize generic types of cosets of type-definable subgroups.

In this paper we develop a theory of stability for $G$-categories (presheaf of categories on the orbit category of $G$), where $G$ is a finite group. We give a description of Mackey functors as $G$-commutative monoids exploit it to…

We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving…

We show that the patterns in the Abelian sandpile are stable. The proof combines the structure theory for the patterns with the regularity machinery for non-divergence form elliptic equations. The stability results allows one to improve…

In this paper, we show how certain ``stability phenomena'' in unpointed model categories provide the sets of homotopy classes with the structure of abelian heaps, i.e. abelian groups without a choice of a zero. In contrast with the…

We shall study the chamber structure of positive cone of the albanese fiber of the moduli spaces of stable objects on an abelian surfaces via the chamber structure of stability conditions.

We give a brief introduction to the relationship between Bridgeland stability conditions and the $K(\pi,1)$ conjecture for Artin groups. These notes have been written as pre-reading for the MFO mini-workshop 2405a: Artin groups meet…