Weak multiplier bimonoids

Gabriella Böhm*, José Gómez-Torrecillas, Stephen Lack

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    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
    Issue number1
    Early online date11 May 2017
    Publication statusPublished - Feb 2018


    • Multiplier bialgebra
    • Weak bialgebra
    • Braided monoidal category


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