Related papers: Cluster categories for topologists
We study the notion of positive and negative complexity of pairs of objects in cluster categories. The first main result shows that the maximal complexity occurring is either one, two or infinite, depending on the representation type of the…
Our aim in this paper is to prove two results related to the three constructions of cluster categories: as orbit categories, as singularity categories and as cosingularity categories. In the first part of the paper, we prove the universal…
Extriangulated categories axiomatize extension-closed subcategories of triangulated categories and generalise both exact categories and triangulated categories. This survey article presents three applications of extriangulated categories to…
We introduce the concept of a pseudo-cluster tilting subcategory from the viewpoint of the fact that the quotient of an exact category by a cluster tilting subcategory is an abelian category. We prove that the quotients in the case of…
These notes provide an introduction to the theory of localization for triangulated categories. Localization is a machinery to formally invert morphisms in a category. We explain this formalism in some detail and we show how it is applied to…
As a first step towards a comprehensive investigation of stellar motions within globular clusters, we present here the results of a study of stellar orbits in a mildly triaxial globular cluster that follows a circular orbit inside a galaxy.…
We introduce $n$-abelian and $n$-exact categories, these are analogs of abelian and exact categories from the point of view of higher homological algebra. We show that $n$-cluster-tilting subcategories of abelian (resp. exact) categories…
We introduce and study mutation of torsion pairs, as a generalization of mutation of cluster tilting objects, rigid objects and maximal rigid objects. It is proved that any mutation of a torsion pair is again a torsion pair. A geometric…
We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to…
Extriangulated categories axiomatize extension-closed subcategories of triangulated categories. We show that the homotopy category of an exact quasi-category can be equipped with a natural extriangulated structure.
We give a combinatorial classification of cluster tilting subcategories and torsion pairs in Igusa--Todorov cluster categories of Dynkin type $A_{ \infty }$.
In this paper we provide an overview of category theory, focussing on applications in physics. The route we follow is motivated by the final goal of understanding anyons and topological QFTs using category theory. This entails introducing…
We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples
A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
Based on homological algebra of Grothendieck categories of enriched functors, two models for Voevodsky's category of big motives with reasonable correspondences are given in this paper.
We develop a general theory of cluster categories, applying to a 2-Calabi-Yau extriangulated category $\mathcal{C}$ and cluster-tilting subcategory $\mathcal{T}$ satisfying only mild finiteness conditions. We show that the structure theory…
We construct relative $3$-Calabi--Yau categories related with higher Teichm\"uller theory. We further study their corresponding cosingularity categories and the additive categorification of the corresponding cluster algebras. The input for…
We study the problem of explainability-first clustering where explainability becomes a first-class citizen for clustering. Previous clustering approaches use decision trees for explanation, but only after the clustering is completed. In…
In this note, I define a notion of a compactly supported object in a triangulated category. I prove a number of propositions relating this to traditional notions of support and give an application to the theory of derived Morita…