Related papers: Torsion models for tensor-triangulated categories
Torsion pairs in the category of finitely presented modules over a noetherian ring can be parametrised by the class of cosilting modules. In this paper, we characterise such modules in terms of their indecomposable summands, providing a new…
We study the composition of Bousfield localizations on a tensor triangulated category stratified via the Balmer-Favi support and with noetherian Balmer spectrum. Our aim is to provide reductions via purely axiomatic arguments, allowing us…
We give several criteria to decide whether a given tensor category is the abelian envelope of a fixed symmetric monoidal category. As a main result we prove that the category of finite-dimensional representations of a semisimple simply…
We introduce the rigid tensor category of tubular partitions, and use it to provide a combinatorial model for the representation category of the quantum automorphism group of a homogeneous rooted tree.
We investigate invertible elements and gradings in braided tensor categories. This leads us to the definition of theta-, product-, subgrading and orbitcategories in order to construct new families of BTC's from given ones. We use the…
We show that in a finite tensor category, the tensor product property holds for support varieties if and only if it holds between indecomposable periodic objects. We apply this to certain Hopf algebras in the form of skew group algebras. In…
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 advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projective resolution as measured by the Frobenius-Perron dimension.…
We prove that any `finite-type' component of a stability space of a triangulated category is contractible. The motivating example of such a component is the stability space of the Calabi--Yau-$N$ category $\mathcal{D}(\Gamma_N Q)$…
We describe several equivalent models for the infinity-category of infinity-local systems of chain complexes over a space using the framework of quasi-categories. We prove that the given models are equivalent as infinity-categories by…
We prove that the map on Balmer spectra induced by a fully faithful geometric functor is a quotient map whose fibers are connected. This is an analogue of the Zariski Connectedness Theorem in algebraic geometry and it can be applied to a…
We define the cohomology and formal deformation theories for algebra and bialgebra categories. We suggest some approaches to finding nontrivial deformations of the categories associated to the quantum groups by the work of Lusztig.
To any triangulated category with tensor product $(K,\otimes)$, we associate a topological space $Spc(K,\otimes)$, by means of thick subcategories of $K$, a la Hopkins-Neeman-Thomason. Moreover, to each open subset $U$ of $Spc(K,\otimes)$,…
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 define the spectrum of a tensor triangulated category $K$ as the set of so-called prime ideals, endowed with a suitable topology. In this very generality, the spectrum is the universal space in which one can define supports for objects…
We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…
Real or complex tensor model observables, the backbone of the tensor theory space, are classical (unitary, orthogonal, symplectic) Lie group invariants. These observables represent as colored graphs, and that representation gives an handle…
Given a noetherian abelian category $\mathcal Z$ of homological dimension two with a tilting object $T$, the abelian category $\mathcal Z$ and the abelian category of modules over $\text{End} (T)^{\textit{op}}$ are related by a sequence of…
This is a continuation of the paper "Modular tensor categories and orbifold theories", arXiv:math.QA/0104242. It discusses orbifold models of conformal filed theory, or, in mathematical language, question of constructing the category of…
Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for…