Related papers: Model theory in compactly generated (tensor-)trian…
We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored *-categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what…
It is known that finite crossed modules provide premodular tensor categories. These categories are in fact modularizable. We construct the modularization and show that it is equivalent to the module category of a finite Drinfeld double.
Given an action of a finite group on a triangulated category, we investigate under which conditions one can construct a linearised triangulated category using DG-enhancements. In particular, if the group is a finite group of automorphisms…
We introduce the main concepts and announce the main results in a theory of tensor products for module categories for a vertex operator algebra. This theory is being developed in a series of papers including hep-th 9309076 and hep-th…
The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning…
Let T be a Hom-finite triangulated Krull-Schmidt category over a field k. Inspired by a definition of Koenig and Liu, we say that a family S of pairwise orthogonal objects in T with trivial endomorphism rings is a simple-minded system if…
In this paper the authors prove fundamental decomposition theorems pertaining to the internal structure of monoidal triangulated categories (M$\Delta$Cs). The tensor structure of an M$\Delta$C enables one to view these categories like…
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…
We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…
We recall the structure of the indecomposable sl(2) modules in the Bernstein-Gelfand-Gelfand category O. We show that all these modules can arise as quantized phase spaces of physical models. In particular, we demonstrate in a path integral…
The goal of this article is to develop the theory of presentable categories and topoi internal to an arbitrary $\infty$-topos $\mathcal{B}$. Our main results are internal analogues of Lurie's and Lurie-Simpson's characterisations of…
We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated…
We provide a new characterization of enriched accessible categories by introducing the two new notions of virtual reflectivity and virtual orthogonality as a generalization of the usual reflectivity and orthogonality conditions for locally…
This paper addresses the problem of describing the structure of tensor C*-categories M with conjugates and irreducible tensor unit. No assumption on the existence of a braided symmetry or on amenability is made. Our assumptions are…
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…
Categorical aspects of the theory of modules over trusses are studied. Tensor product of modules over trusses is defined and its existence established. In particular, it is shown that bimodules over trusses form a monoidal category. Truss…
In the generality of a rigidly-compactly generated tensor triangulated category, we introduce semi-Bousfield classes in terms of the vanishing of the tensor product in positive degrees with respect to a fixed reasonable $t$-structure. We…
We extend Ng's characterisation of torsion pairs in the 2-Calabi-Yau triangulated category generated by a 2-spherical object to the characterisation of torsion pairs in the w-Calabi-Yau triangulated category, $T_w$, generated by a…
In previous work (Coulembier--Flake 2024), the authors conjectured that the tensor product of an arbitrary finite-dimensional modular representation of an elementary abelian $p$-group with the biggest non-projective restricted Steinberg…
Let $\mathcal{X}$ be a skeletally small additive category. Using the canonical equivalence between two different presentations of the free abelian category over $\mathcal{X}$, we give a new and simple characterization of definable…