Monoidal supercategories
type: Item
instance of: scholarly article
title: Monoidal supercategories
zbMATH Open document ID: 1396.17012
author: Jonathan Brundan
author: Alexander P. Ellis
published in: Communications in Mathematical Physics
publication date: 2017-04-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1603.05928
review text: By now, there are several notions in the literature which are supposed to describe what should be called a super monoidal category. The goal of the paper under review is to clarify these notions and connections between them and in this way to develop a unified axiomatization for \(2\)-supercategories, that is \(2\)-categories enriched in vector superspaces, and related formal constructions. In particular, the paper discusses a superanalogue of the notion of Drinfeld center and considers \(2\)-supercategories with a fixed distinguished involution in its Drinfeld center. Gradings and Grothendieck groups in the supersetting are also discussed.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 18D05
zbMATH DE Number: 6705472
zbMATH Keywords: superalgebra
zbMATH Keywords: supercategory
zbMATH Keywords: superfunctor
zbMATH Keywords: 2-supercategory
zbMATH Keywords: superadditive envelope
zbMATH Keywords: monoidal supercategory
MaRDI profile type: Publication
OpenAlex ID: W3037016430
arXiv ID: 1603.05928
cites work: Q4523528
cites work: On the definition of Kac-Moody 2-category
cites work: A basis theorem for the affine oriented Brauer category and its cyclotomic quotients
cites work: Super Kac–Moody 2‐categories
cites work: Tensor Product Categorifications and the Super Kazhdan–Lusztig Conjecture
cites work: Webs and quantum skew Howe duality
cites work: Quantum supergroups. IV: The modified form
cites work: Canonical basis for quantum \(\mathfrak{osp}(1|2)\)
cites work: Soergel calculus
cites work: Diagrammatics for Coxeter groups and their braid groups
cites work: Supercategorification of quantum Kac-Moody algebras. I, II
cites work: Tensor Categories
cites work: Mixed Schur-Weyl-Sergeev duality for queer Lie superalgebras
cites work: Q4679165
cites work: A categorification of quantum \(\text{sl}(n)\)
cites work: The marked Brauer category
cites work: Spiders for rank 2 Lie algebras
cites work: Basic Category Theory
cites work: The Brauer category and invariant theory
cites work: Q5639839
cites work: Q4342624
cites work: Drinfeld centers for bicategories
cites work: Quiver Hecke algebras and 2-Lie algebras.
cites work: KAZHDAN-LUSZTIG-POLYNOME UND UNZERLEGBARE BIMODULN ÜBER POLYNOMRINGEN
cites work: Fermionic 6j-symbols in superfusion categories
cites work: The representation theory of the Temperley-Lieb algebras
DOI: 10.1007/S00220-017-2850-9
description: scientific article