Hopf polyads, Hopf categories and Hopf group monoids viewed as Hopf monads

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We associate, in a functorial way, a monoidal bicategory SpanjV to any monoidal bicategory V. Two examples of this construction are of particular interest: Hopf polyads of [Bruguières 2015] can be seen as Hopf monads in Span|Cat while Hopf group monoids in the spirit of [Zunino 2004, Turaev 2000] in a braided monoidal category V, and Hopf categories of [Batista-Caenepeel-Vercruysse 2016] over V both turn out to be Hopf monads in Span|V. Hopf group monoids and Hopf categories are Hopf monads on a distinguished type of monoidales fitting the framework of [Böhm-Lack 2016]. These examples are related by a monoidal pseudofunctor V → Cat.

Original languageEnglish
Pages (from-to)1229-1257
Number of pages29
JournalTheory and Applications of Categories
Volume32
Publication statusPublished - Sep 18 2017

Fingerprint

Monads
Monoids
Bicategory
Monoidal Category

Keywords

  • Hopf category
  • Hopf group algebra
  • Hopf monad
  • Hopf polyad
  • Monoidal bicategory
  • Monoidale

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

Hopf polyads, Hopf categories and Hopf group monoids viewed as Hopf monads. / Böhm, G.

In: Theory and Applications of Categories, Vol. 32, 18.09.2017, p. 1229-1257.

Research output: Contribution to journalArticle

@article{77c93d16a80a4084b501f67fba8afb78,
title = "Hopf polyads, Hopf categories and Hopf group monoids viewed as Hopf monads",
abstract = "We associate, in a functorial way, a monoidal bicategory SpanjV to any monoidal bicategory V. Two examples of this construction are of particular interest: Hopf polyads of [Brugui{\`e}res 2015] can be seen as Hopf monads in Span|Cat while Hopf group monoids in the spirit of [Zunino 2004, Turaev 2000] in a braided monoidal category V, and Hopf categories of [Batista-Caenepeel-Vercruysse 2016] over V both turn out to be Hopf monads in Span|V. Hopf group monoids and Hopf categories are Hopf monads on a distinguished type of monoidales fitting the framework of [B{\"o}hm-Lack 2016]. These examples are related by a monoidal pseudofunctor V → Cat.",
keywords = "Hopf category, Hopf group algebra, Hopf monad, Hopf polyad, Monoidal bicategory, Monoidale",
author = "G. B{\"o}hm",
year = "2017",
month = "9",
day = "18",
language = "English",
volume = "32",
pages = "1229--1257",
journal = "Theory and Applications of Categories",
issn = "1201-561X",
publisher = "Mount Allison University",

}

TY - JOUR

T1 - Hopf polyads, Hopf categories and Hopf group monoids viewed as Hopf monads

AU - Böhm, G.

PY - 2017/9/18

Y1 - 2017/9/18

N2 - We associate, in a functorial way, a monoidal bicategory SpanjV to any monoidal bicategory V. Two examples of this construction are of particular interest: Hopf polyads of [Bruguières 2015] can be seen as Hopf monads in Span|Cat while Hopf group monoids in the spirit of [Zunino 2004, Turaev 2000] in a braided monoidal category V, and Hopf categories of [Batista-Caenepeel-Vercruysse 2016] over V both turn out to be Hopf monads in Span|V. Hopf group monoids and Hopf categories are Hopf monads on a distinguished type of monoidales fitting the framework of [Böhm-Lack 2016]. These examples are related by a monoidal pseudofunctor V → Cat.

AB - We associate, in a functorial way, a monoidal bicategory SpanjV to any monoidal bicategory V. Two examples of this construction are of particular interest: Hopf polyads of [Bruguières 2015] can be seen as Hopf monads in Span|Cat while Hopf group monoids in the spirit of [Zunino 2004, Turaev 2000] in a braided monoidal category V, and Hopf categories of [Batista-Caenepeel-Vercruysse 2016] over V both turn out to be Hopf monads in Span|V. Hopf group monoids and Hopf categories are Hopf monads on a distinguished type of monoidales fitting the framework of [Böhm-Lack 2016]. These examples are related by a monoidal pseudofunctor V → Cat.

KW - Hopf category

KW - Hopf group algebra

KW - Hopf monad

KW - Hopf polyad

KW - Monoidal bicategory

KW - Monoidale

UR - http://www.scopus.com/inward/record.url?scp=85031112677&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85031112677&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85031112677

VL - 32

SP - 1229

EP - 1257

JO - Theory and Applications of Categories

JF - Theory and Applications of Categories

SN - 1201-561X

ER -