Related papers: Some functors preserving exceptionality
Certain classical generating functions for elements of reflection groups can be expressed using fundamental invariants called exponents. We give new analogues of such generating functions that accommodate orbits of reflecting hyperplanes…
For each recollement of triangulated categories, there is an epivalence between the middle category and the comma category associated to a triangle functor from the category on the right to the category on the left. For a morphic…
Tilting modules, generalising the notion of progenerator, furnish equivalences between pieces of module categories. This paper is dedicated to study how much these pieces say about the whole category. We will survey the existing results in…
After constructing a splitting tower for separable commutative ring objects in tensor-triangulated categories, we define and study their degree.
We classify simple modules over the Green biset functor of section Burnside rings.
This is the third part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part III), we introduce and study…
We extend Deligne's notion of determinant functor to tensor triangulated categories. Specifically, to account for the multiexact structure of the tensor, we define a determinant functor on the 2-multicategory of triangulated categories and…
We study a 2-functor that assigns to a bimodule category over a finite k-linear tensor category a k-linear abelian category. This 2-functor can be regarded as a category-valued trace for 1-morphisms in the tricategory of finite tensor…
We construct an exact functor from the category of Harish-Chandra modules of $\mathrm{GL}_n(\mathbb C)$ to the category of finite-dimensional modules of graded Hecke algebras of type A. We show that the functor preserves parabolically…
For a regular normal element in an arbitrary ring, we study the category of its module factorizations. The cokernel functor relates module factorizations with Gorenstein projective components to Gorenstein projective modules over the…
We construct Nakayama functors on proper abelian subcategories of triangulated categories with a Serre functor using approximation theory. This, in turn, allows for the construction of Auslander-Reiten translates. As a result, we prove that…
We compare the bicategory of spans with that of bisets (a.k.a. bimodules, distributors, profunctors) in the context of finite groupoids. We construct in particular a well-behaved pseudo-functor from spans to bisets. This yields an…
In the paper, we focus on the silting properties and the combinatorial properties of silting and Gorenstein, which is called Gorenstein silting, where the main tools used are recollements of module categories and tensor products. For a ring…
Let $A={\rm \mathbb{k}}Q/\mathcal{I}$ be a gentle algebra. We provide a bijection between non-projective indecomposable Gorenstein projective modules over $A$ and special recollements induced by an arrow $a$ on any full-relational oriented…
For any finite group G with a finite G-set X and a modular tensor category C we construct a part of the algebraic structure of an associated G-equivariant monoidal category: For any group element g in G we exhibit the module category…
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…
In this paper we give construct good moduli spaces for constructible sheaves and Stokes functors. Derived enhancement of such are also considered.
In persistent topology, q-tame modules appear as a natural and large class of persistence modules indexed over the real line for which a persistence diagram is definable. However, unlike persistence modules indexed over a totally ordered…
In this short note we observe that the Serre functor on the residual category of a complete intersection can be easily described in the framework of hybrid models. Using this description we recover some recent results of Kuznetsov and…
Additive categories play a fundamental role in mathematics and related disciplines. Given an additive category equipped with a biadditive functor, one can construct its category of extensions, which encodes important structural information.…