Abstract
The central object studied in this paper is a multiplier bimonoid in a braided monoidal category \(\mathcal {C}\), 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 \(\mathcal {C}\), we introduce a category \(\mathcal {M}\) whose objects are certain semigroups in \(\mathcal {C}\) and whose morphisms A→B can be regarded as suitable multiplicative morphisms from A to the multiplier monoid of B. We equip this category \(\mathcal {M}\) with a monoidal structure and describe multiplier bimonoids in \(\mathcal {C}\) (whose structure morphisms belong to a distinguished class of regular epimorphisms) as certain comonoids in \(\mathcal {M}\). This provides us with one possible notion of morphism between such multiplier bimonoids.
Similar content being viewed by others
References
Böhm, G., Lack, S.: A simplicial approach to multiplier structures, preprint available at arXiv:1512.01259
Böhm, G., Gómez-Torrecillas, J., Lack, S.: Weak multiplier bimonoids, in preparation
Böhm, G., Gómez-Torrecillas, J., López-Centella, E.: Weak multiplier bialgebras. Trans. Amer. Math. Soc. 367(12), 8681–8721 (2015)
Böhm, G., Lack, S.: Multiplier bialgebras in braided monoidal categories. J. Algebra 423, 853–889 (2015)
Buckley, M., Garner, R., Lack, S., Street, R.: The Catalan simplicial set. Math. Proc. Camb. Phil. Soc. 158, 211–222 (2015)
Janssen, K., Vercruysse, J.: Multiplier bi- and Hopf algebras. J. Algebra Appl. 9(2), 275–303 (2010)
Van Daele, A.: Multiplier Hopf algebras. Trans. Amer. Math. Soc. 342, 917–932 (1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Böhm, G., Lack, S. A Category of Multiplier Bimonoids. Appl Categor Struct 25, 279–301 (2017). https://doi.org/10.1007/s10485-016-9429-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10485-016-9429-z