Related papers: Hereditary $n$-exangulated categories
We introduce Manifold tensor categories, which make precise the notion of a tensor category with a manifold of simple objects. A basic example is the category of vector spaces graded by a Lie group. Unlike classic tensor category theory,…
We define and investigate a class of Koszul quasi-hereditary algebras for which there is a natural equivalence between the bounded derived category of graded modules and the bounded derived category of graded modules over (a proper version…
We give a reduction technique for silting intervals in extriangulated categories, which we call "silting interval reduction". It provides a reduction technique for tilting subcategories when the extriangulated categories are exact…
The Euler characteristic was defined for finite strict n-categories by Leinster using the theory of enriched categories. This was an extension of some of his earlier work, which defined Euler characteristic for finite categories. Building…
We introduce extriangulated factorization systems in extriangulated categories and show that there exists a bijection between $s$-torsion pairs and extriangulated factorization systems. We also consider the gluing of $s$-torsion pairs and…
For a tensor triangulated category and any regular cardinal $\alpha$ we study the frame of $\alpha$-localizing tensor ideals and its associated space of points. For a well-generated category and its frame of localizing tensor ideals we…
Let C be an extriangulated category. We prove that two quotient categories of extriangu?lated categories induced by selforthogonal subcategories are equivalent to module categories by restriction of two functors E and Hom, respectively.…
We introduce Toda brackets for n-angulated categories and show that the various definitions of Toda brackets coincide. We prove juggling formulas for these Toda brackets generalizing the triangulated case. Following that, we generalize a…
We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.
We recognise Harada's generalized categories of diagrams as a particular case of modules over a monad defined on a finite direct product of additive categories. We work in the dual (albeit formally equivalent) situation, that is, with…
In this work we introduce the notion of higher $\mathbb{E}$-extension groups for an extriangulated category $\mathcal{C}$ and study the quotients $\mathcal{X}_{n+1}^{\vee}/[\mathcal{X}]$ and $\mathcal{X}_{n+1}^{\wedge}/[\mathcal{X}]$ when…
The notion of relative derived category with respect to a subcategory is introduced. A triangle-equivalence, which extends a theorem of Gao and Zhang [Gorenstein derived categories, \emph{J. Algebra} \textbf{323} (2010) 2041-2057] to the…
We classify the imaginaries in a large class of equicharacteristic zero henselian valued fields that contain all those with bounded inertia group, and more. To do so, we consider a mix of sorts introduced in earlier works of the two authors…
We introduce a new type of categorical object called a \emph{hom-tensor category} and show that it provides the appropriate setting for modules over an arbitrary hom-bialgebra. Next we introduce the notion of \emph{hom-braided category} and…
We show that Kuznetsov--Shinder's notion of deformation absorption of singularities leads to a new approach for studying the bounded derived category of a hereditary order on a curve. The starting point is a hereditary order which can be…
We give analogues of the Auslander correspondence for two classes of triangulated categories satisfying certain finiteness conditions. The first class is triangulated categories with additive generators and we consider their endomorphism…
We study finiteness conditions in Grothendieck categories by introducing the concepts of objects of type $\text{FP}_n$ and studying their closure properties with respect to short exact sequences. This allows us to propose a notion of…
We classify certain $\mathbb{Z}_2 $-graded extensions of generalized Haagerup categories in terms of numerical invariants satisfying polynomial equations. In particular, we construct a number of new examples of fusion categories, including:…
In this paper, firstly, we introduce a higher-dimensional analogue of hypergraphs, namely $\omega$-hypergraphs. This notion is thoroughly flexible because unlike ordinary $\omega$-graphs, an n-dimensional edge called an n-cell has many…
In this paper, we study (complete) cotorsion pairs in extriangulated categories. First, we study a relationship between an interval of the poset of cotorsion pairs and the poset of cotorsion pairs in the heart associated to the interval.…