Related papers: Modular Categories
We propose a categorical and algebraic study of quantale modules. The results and constructions presented are also applied to abstract algebraic logic and to image processing tasks.
This article develops a practical technique for studying representations of $\Bbbk$-linear categories arising in the categorification of quantum groups. We work in terms of locally unital algebras which are $\mathbb{Z}$-graded with graded…
This is the fourth (and last) prepublication version of a book on derived categories, that will be published by Cambridge University Press. The purpose of the book is to provide solid foundations for the theory of derived categories, and to…
Modular categories are a well-known source of quantum 3-manifold invariants. In this paper we study structures on modular categories which allow to define refinements of quantum 3-manifold invariants involving cohomology classes or…
In this work we develop some categorical aspects of the double structure of a module.
These are lecture notes of the course in infinity categories given in the fall 2016 at Weizmann Institute.
This is an overview of our series of papers on the modular generalized Springer correspondence. It is an expansion of a lecture given by the second author in the Fifth Conference of the Tsinghua Sanya International Mathematics Forum, Sanya,…
These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.
These are expanded lecture notes from lectures given at the Workshop on higher structures at MATRIX Melbourne. These notes give an introduction to Feynman categories and their applications. Feynman categories give a universal categorical…
We study the classification of submodules of module categories over monoidal categories, extending ideas of Coulembier on the classification of tensor ideals in monoidal categories. We develop a framework that applies to module categories…
A non-self-contained gathering of notes on category theory, including the definition of locally cartesian closed category, of the cartesian structure in slice categories, or of the pseudo-cartesian structure on Eilenberg-Moore categories.…
We classify the module categories over the double (possibly twisted) of a finite group.
This thesis is about the problem of compositionality in distributional semantics. Distributional semantics presupposes that the meanings of words are a function of their occurrences in textual contexts. It models words as distributions over…
In this paper, we use basic formal variable techniques to study certain categories of modules for the toroidal Lie algebra $\tau$. More specifically, we define and study two categories $\mathcal{E}_{\tau}$ and $\mathcal{C}_{\tau}$ of…
This paper describes a computational framework for a grammar architecture in which different linguistic domains such as morphology, syntax, and semantics are treated not as separate components but compositional domains. Word and phrase…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
This is a position paper written as an introduction to the special volume on quantum algorithms I edited for the journal Mathematical Structures in Computer Science (Volume 20 - Special Issue 06 (Quantum Algorithms), 2010).
We give a review of some recent developments in the theory of tensor categories. The topics include realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory,…
We study modular forms of some congruence subgroups. In this paper, we treat the cases level is 2-power, 3-power or 5. Structures of graded rings and many identities of infinite sum or infinite product are given. Theory of rational (1/3,…
This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…