Related papers: On the applicability of logarithmic tensor categor…
We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples
We develop a systematic study of the schur tensor product both in the category of operator spaces and in that of $C^*$-algebras.
The theory of Selberg zeta functions is generalized to higher rank spaces. Applications towards analytic torsion numbers are given.
We introduce (partially) ordered Grothendieck categories and apply results on their structure to the study of categories of representations of the Mackey Lie algebra of infinite matrices $\mathfrak{gl}^M\left(V,V_*\right)$. Here…
We show that if $\mathcal{U}$ and $\mathcal{V}$ are locally finite abelian categories of modules for vertex operator algebras $U$ and $V$, respectively, then the Deligne tensor product of $\mathcal{U}$ and $\mathcal{V}$ can be realized as a…
In this paper we state some applications of Gr-category theory on the classification of crossed modules and on the classification of extensions of groups of the type of a crossed module.
The category of modules over a string algebra is equipped with a tensor product defined point-wise and arrow-wise in terms of the underlying quiver. In the present article we investigate how this tensor product interacts with the…
In this paper we study the tensor product for MV-algebras, the algebraic structures of \L ukasiewicz $\infty$-valued logic. Our main results are: the proof that the tensor product is preserved by the categorical equivalence between the…
We present a survey of some developments in the general area of category-theoretic approaches to the theory of computation, with a focus on topics and ideas particularly close to the interests of Jim Lambek.
In this paper we classify indecomposable modules for the Lie algebra of vector fields on a torus that admit a compatible action of the algebra of functions. An important family of such modules is given by spaces of jets of tensor fields.
We classify blocks of categories of weight and generalized weight modules of algebras of twisted differential operators on P^n. Necessary and sufficient conditions for these blocks to be tame and proofs that some of the blocks are Koszul…
In this paper, we show Kazhdan-Lusztig categories, that is, the categories of lower bounded generalized weight modules for certain affine vertex operator superalgebras that are locally finite modules of the underlying finite dimensional Lie…
IIn this paper, extensions of affine vertex operator algebras $L_{sl_3}(k,0)$, $k\in \mathbb{Z}_+$, are classified by modular invariants.
We introduce the concept of Hom-associative algebra structures in Loday-Pirashvili category.The cohomology theory of Hom-associative algebras in this category is studied.Some applications on deformation and abelian extension theory are…
In this article we give application of closure operators in category of modules. Our main result shows that every subcategory A of injective modules of R-mod (under a mild condition) induces a torsion theory of R-mod.
In this paper, we study a new kind of vertex operator algebra related to the twisted Heisenberg-Virasoro algebra, which we call the twisted Heisenberg-Virasoro vertex operator algebra, and its modules. Specifically, we present some results…
Operator systems connect operator algebra, free semialgebraic geometry and quantum information theory. In this work we generalize operator systems and many of their theorems. While positive semidefinite matrices form the underlying…
This article serves as a preliminary introduction to the design of a new, open-source applied and computational category theory framework, named Categorica, built on top of the Wolfram Language. Categorica allows one to configure and…
We define the notion of whiskered categories and groupoids, showing that whiskered groupoids have a commutator theory. So also do whiskered $R$-categories, thus answering questions of what might be `commutative versions' of these theories.…
We prove a recursive identity involving formal iterated logarithms and formal iterated exponentials. These iterated logarithms and exponentials appear in a natural extension of the logarithmic formal calculus used in the study of…