### Abstract

The central object studied in this paper is a multiplier bimonoid in a braided monoidal category C, introduced and studied in Böhm and Lack (J. Algebra 423, 853–889 2015). Adapting the philosophy in Janssen and Vercruysse (J. Algebra Appl. 9(2), 275–303 2010), and making some mild assumptions on the category C, we introduce a category ℳ whose objects are certain semigroups in C and whose morphisms A→B can be regarded as suitable multiplicative morphisms from A to the multiplier monoid of B. We equip this category ℳ with a monoidal structure and describe multiplier bimonoids in C (whose structure morphisms belong to a distinguished class of regular epimorphisms) as certain comonoids in ℳ. This provides us with one possible notion of morphism between such multiplier bimonoids.

Language | English |
---|---|

Pages | 279-301 |

Number of pages | 23 |

Journal | Applied Categorical Structures |

Volume | 25 |

Issue number | 2 |

Early online date | 24 Mar 2016 |

DOIs | |

State | Published - 2017 |

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### Cite this

*Applied Categorical Structures*,

*25*(2), 279-301. DOI: 10.1007/s10485-016-9429-z

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*Applied Categorical Structures*, vol 25, no. 2, pp. 279-301. DOI: 10.1007/s10485-016-9429-z

**A category of multiplier bimonoids.** / Böhm, Gabriella; Lack, Stephen.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A category of multiplier bimonoids

AU - Böhm,Gabriella

AU - Lack,Stephen

PY - 2017

Y1 - 2017

N2 - The central object studied in this paper is a multiplier bimonoid in a braided monoidal category C, introduced and studied in Böhm and Lack (J. Algebra 423, 853–889 2015). Adapting the philosophy in Janssen and Vercruysse (J. Algebra Appl. 9(2), 275–303 2010), and making some mild assumptions on the category C, we introduce a category ℳ whose objects are certain semigroups in C and whose morphisms A→B can be regarded as suitable multiplicative morphisms from A to the multiplier monoid of B. We equip this category ℳ with a monoidal structure and describe multiplier bimonoids in C (whose structure morphisms belong to a distinguished class of regular epimorphisms) as certain comonoids in ℳ. This provides us with one possible notion of morphism between such multiplier bimonoids.

AB - The central object studied in this paper is a multiplier bimonoid in a braided monoidal category C, introduced and studied in Böhm and Lack (J. Algebra 423, 853–889 2015). Adapting the philosophy in Janssen and Vercruysse (J. Algebra Appl. 9(2), 275–303 2010), and making some mild assumptions on the category C, we introduce a category ℳ whose objects are certain semigroups in C and whose morphisms A→B can be regarded as suitable multiplicative morphisms from A to the multiplier monoid of B. We equip this category ℳ with a monoidal structure and describe multiplier bimonoids in C (whose structure morphisms belong to a distinguished class of regular epimorphisms) as certain comonoids in ℳ. This provides us with one possible notion of morphism between such multiplier bimonoids.

KW - Braided monoidal category

KW - Multiplier bimonoid

UR - http://www.scopus.com/inward/record.url?scp=84961657977&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP130101969

UR - http://purl.org/au-research/grants/arc/FT110100385

U2 - 10.1007/s10485-016-9429-z

DO - 10.1007/s10485-016-9429-z

M3 - Article

VL - 25

SP - 279

EP - 301

JO - Applied Categorical Structures

T2 - Applied Categorical Structures

JF - Applied Categorical Structures

SN - 0927-2852

IS - 2

ER -