Year: 2026
Type: preprint
Abstract: We study braidings and infinitesimal braidings on categories of bi(co)modules and tetramodules, and their compatibility with duoidal structures. For an arbitrary coalgebra, we classify braidings on its category of bicomodules with the cotensor product in terms of canonical $R$-forms, dualizing the classification for bimodules obtained by Agore, Caenepeel, and Militaru. Every such braiding is a symmetry and admits only the zero infinitesimal braiding. We construct duoidal structures on categories of bi(co)modules and tetramodules over bimonoids in braided monoidal categories under suitable assumptions on equalizers and coequalizers. We then introduce pre-Cartier duoidal categories and their one-sided variants. We establish obstructions to compatible braidings for tetramodules, construct nonzero one-sided pre-Cartier structures on bi(co)modules, and give a pre-Cartier duoidal example with distinct monoidal products and a nonzero infinitesimal braiding.
Source: arXiv (Cornell University)
Authors: Sciandra, Andrea, Simons, Lukas
Institutions: Université Libre de Bruxelles, Vrije Universiteit Brussel
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214238098