Braidings, duoidal categories and pre-Cartier structures for bi(co)modules

@misc{sciandra2026braidings,
  title = {{Braidings, duoidal categories and pre-Cartier structures for bi(co)modules}},
  author = {Andrea Sciandra and Lukas Simons},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28304},
  eprint = {2609.28304},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28304},
}

TY  - UNPB
TI  - Braidings, duoidal categories and pre-Cartier structures for bi(co)modules
AU  - Andrea Sciandra
AU  - Lukas Simons
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28304
UR  - https://arxiv.org/abs/2609.28304
AB  - 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.
ER  -