Related papers: Triangulation, Persistence, and Fukaya categories
We provide a framework to triangulate subfactor categories of additive categories with additive endofunctors. It is proved that such a framework is sufficiently flexible to cover many instances in algebra and geometry where abelian, exact…
This paper is an expository account of the theory of stable infinity categories. We prove that the homotopy category of a stable infinity category is triangulated, and that the collection of stable infinity categories is closed under a…
The category of modules over the endomorphism algebra of a rigid object in a Hom-finite triangulated category C has been given two different descriptions: On the one hand, as shown by Osamu Iyama and Yuji Yoshino, it is equivalent to an…
We find stability conditions ([Do], [Br]) on some derived categories of differential graded modules over a graded algebra studied in [RZ], [KS]. This category arises in both derived Fukaya categories and derived categories of coherent…
Let $R$ be a commutative ring. A full additive subcategory $\C$ of $R$-modules is triangulated if whenever two terms of a short exact sequence belong to $\C$, then so does the third term. In this note we give a classification of…
In this paper, motivated by symplectic topology, we explore categorical entropy and present two main results. The first result establishes a relation between categorical entropies of functors on a category and its localization.…
Persistence diagram (PD) bundles, a generalization of vineyards, were introduced as a way to study the persistent homology of a set of filtrations parameterized by a topological space $B$. In this paper, we present an algorithm for…
It is well known that "Fukaya category" is in fact an $A_{\infty}$-pre-category in sense of Kontsevich and Soibelman \cite{KS}. The reason is that in general the morphism spaces are defined only for transversal pairs of Lagrangians, and…
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…
We prove that a triangulated category which is the underlying category of a stable derivator has a filtered enhancement, providing an affirmative answer to a conjecture in [3].
Stability conditions on triangulated categories were introduced by Bridgeland as a 'continuous' generalisation of t-structures. The set of locally-finite stability conditions on a triangulated category is a manifold which has been studied…
We show that a persistence module (for a totally ordered indexing set) consisting of finite-dimensional vector spaces is a direct sum of interval modules. The result extends to persistence modules with the descending chain condition on…
Modular categories are a well-known source of quantum 3-manifold invariants. In this paper we study structures on modular categories which allow to define refinements of quantum 3-manifold invariants involving cohomology classes or…
We introduce a new notion of persistence modules endowed with operators. It encapsulates the additional structure on Floer-type persistence modules coming from the intersection product with classes in the ambient (quantum) homology, along…
Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In…
A rank-three tensor model in canonical formalism has recently been proposed. The model describes consistent local-time evolutions of fuzzy spaces through a set of first-class constraints which form an on-shell closed algebra with structure…
Given a triangulation of a polygon P with n vertices, we associate an ice quiver with potential such that the associated Jacobian algebra has the structure of a Gorenstein tiled K[x]-order L. Then we show that the stable category of the…
In a recent collaboration, Hiroki Matsui and the author introduced a new proof of the reconstruction theorem of Bondal-Orlov and Ballard, using Matsui's construction of a ringed space associated to a triangulated category. This paper first…
In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we…
We give a characterisation of those local not necessary commutative rings, for which the category of projective modules admits a triangulation with the identity as translation functor. By "admits a triangulation" we mean that the category…