Results 51 to 60 of about 5,500 (151)

A higher-dimensional categorical perspective on 2-crossed modules

Demonstratio Mathematica
In this study, we will express the 2-crossed module of groups from a higher-dimensional categorical perspective. According to simplicial homotopy theory, a 2-crossed module is the Moore complex of a 2-truncated simplicial group.
Özel Emre, Arslan Ummahan Ege, İlker Akça İbrahim   +2 more
doaj   +1 more source

The Picard group in equivariant homotopy theory via stable module categories

Journal of Topology, Volume 18, Issue 2, June 2025.
Abstract We develop a mechanism of “isotropy separation for compact objects” that explicitly describes an invertible G$G$‐spectrum through its collection of geometric fixed points and gluing data located in certain variants of the stable module category.
Achim Krause
wiley   +1 more source

The Temperley–Lieb tower and the Weyl algebra

Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.
Abstract We define a monoidal category W${\mathbf {W}}$ and a closely related 2‐category 2Weyl${\mathbf {2Weyl}}$ using diagrammatic methods. We show that 2Weyl${\mathbf {2Weyl}}$ acts on the category TL:=⨁nTLn−mod$\mathbf {TL}:=\bigoplus _n \operatorname{TL}_n\mathrm{-mod}$ of modules over Temperley–Lieb algebras, with its generating 1‐morphisms ...
Matthew Harper, Peter Samuelson
wiley   +1 more source

On the parameterized Tate construction

Journal of Topology, Volume 18, Issue 1, March 2025.
Abstract We introduce and study a genuine equivariant refinement of the Tate construction associated to an extension Ĝ$\widehat{G}$ of a finite group G$G$ by a compact Lie group K$K$, which we call the parameterized Tate construction (−)tGK$(-)^{t_G K}$.
J. D. Quigley, Jay Shah
wiley   +1 more source

Categorification of the Kauffman bracket skein module of I-bundles over surfaces

, 2004
Khovanov defined graded homology groups for links L in R^3 and showed that their polynomial Euler characteristic is the Jones polynomial of L. Khovanov's construction does not extend in a straightforward way to links in I-bundles M over surfaces F not D ...
Adam S Sikora, Asaeda, Asaeda, Jozef H Przytycki, Listing, Marta M Asaeda, Przytycki, Viro   +7 more
core   +1 more source

Cluster categories for completed infinity‐gons I: Categorifying triangulations

Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.
Abstract Paquette and Yıldırım recently introduced triangulated categories of arcs in completed infinity‐gons, which are discs with an infinite closed set of marked points on their boundary. These categories have many features in common with the cluster categories associated to discs with different sets of marked points. In particular, they have (weak)
İlke Çanakçı, Martin Kalck, Matthew Pressland   +2 more
wiley   +1 more source

String Diagrams and Categorification

, 2020
These are lectures notes for a mini-course given at the conference Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras, and Categorification in June 2018. The goal is to introduce the reader to string diagram techniques for monoidal categories, with an emphasis on their role in categorification.
openaire   +2 more sources

Derived equivalences for symmetric groups and sl\_2-categorification [PDF]

, 2004
We define and study sl\_2-categorifications on abelian categories. We show in particular that there is a self-derived (even homotopy) equivalence categorifying the adjoint action of the simple reflection.
Chuang, Joseph, Rouquier, Raphael
core   +4 more sources

On finite generation in magnitude (co)homology and its torsion

Bulletin of the London Mathematical Society, Volume 56, Issue 11, Page 3434-3451, November 2024.
Abstract The aim of this paper is to apply the framework developed by Sam and Snowden to study structural properties of graph homologies, in the spirit of Ramos, Miyata and Proudfoot. Our main results concern the magnitude homology of graphs introduced by Hepworth and Willerton, and we prove that it is a finitely generated functor (on graphs of bounded
Luigi Caputi, Carlo Collari
wiley   +1 more source

Categorifications from planar diagrammatics

, 2010
A diagrammatic presentation of functors and natural transformations and the virtues of biadjointness are discussed. We then review a graphical description of the category of Soergel bimodules and a diagrammatic categorification of positive halves of ...
Khovanov, Mikhail
core   +1 more source