Weak Multiplier Bimonoids

G. Böhm, José Gómez-Torrecillas, Stephen Lack

Research output: Contribution to journalArticle

Abstract

Based on the novel notion of ‘weakly counital fusion morphism’, regular weak multiplier bimonoids in braided monoidal categories are introduced. They generalize weak multiplier bialgebras over fields (Böhm et al. Trans. Amer. Math. Soc. 367, 8681–8721, 2015) and multiplier bimonoids in braided monoidal categories (Böhm and Lack, J. Algebra 423, 853–889, 2015). Under some assumptions the so-called base object of a regular weak multiplier bimonoid is shown to carry a coseparable comonoid structure; hence to possess a monoidal category of bicomodules. In this case, appropriately defined modules over a regular weak multiplier bimonoid are proven to constitute a monoidal category with a strict monoidal forgetful type functor to the category of bicomodules over the base object. Braided monoidal categories considered include various categories of modules or graded modules, the category of complete bornological spaces, and the category of complex Hilbert spaces and continuous linear transformations.

Original languageEnglish
Pages (from-to)47-111
Number of pages65
JournalApplied Categorical Structures
Volume26
Issue number1
DOIs
Publication statusPublished - Feb 1 2018

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Monoidal Category
Linear transformations
Hilbert spaces
Algebra
Multiplier
Fusion reactions
Module
Graded Module
Bialgebra
Linear transformation
Morphism
Functor
Fusion
Hilbert space
Generalise

Keywords

  • Braided monoidal category
  • Multiplier bialgebra
  • Weak bialgebra

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Weak Multiplier Bimonoids. / Böhm, G.; Gómez-Torrecillas, José; Lack, Stephen.

In: Applied Categorical Structures, Vol. 26, No. 1, 01.02.2018, p. 47-111.

Research output: Contribution to journalArticle

Böhm, G, Gómez-Torrecillas, J & Lack, S 2018, 'Weak Multiplier Bimonoids', Applied Categorical Structures, vol. 26, no. 1, pp. 47-111. https://doi.org/10.1007/s10485-017-9481-3
Böhm, G. ; Gómez-Torrecillas, José ; Lack, Stephen. / Weak Multiplier Bimonoids. In: Applied Categorical Structures. 2018 ; Vol. 26, No. 1. pp. 47-111.
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