English

Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory

Category Theory 2021-07-23 v1 Algebraic Topology K-Theory and Homology Quantum Algebra

Abstract

Bimonoidal categories are categorical analogues of rings without additive inverses. They have been actively studied in category theory, homotopy theory, and algebraic KK-theory since around 1970. There is an abundance of new applications and questions of bimonoidal categories in mathematics and other sciences. This work provides a unified treatment of bimonoidal and higher ring-like categories, their connection with algebraic KK-theory and homotopy theory, and applications to quantum groups and topological quantum computation. With ample background material, extensive coverage, detailed presentation of both well-known and new theorems, and a list of open questions, this work is a user friendly resource for beginners and experts alike.

Keywords

Cite

@article{arxiv.2107.10526,
  title  = {Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory},
  author = {Niles Johnson and Donald Yau},
  journal= {arXiv preprint arXiv:2107.10526},
  year   = {2021}
}

Comments

This is an abridged version of the book for arxiv.org that contains the full list of open questions together with front and back matters. The complete pdf version is available on the authors' web pages: https://nilesjohnson.net/En-monoidal or https://u.osu.edu/yau.22/main

R2 v1 2026-06-24T04:25:22.028Z