Publication: AMS Surveys and Monographs Volumes 283–285 (2024).

Preprint: Download three volumes (pdf, 7Mb).

Update 2024-06-27:
1. Minor reformatting and typo fixes

See change log for further details.

Bimonoidal categories are categorical analogues of rings without additive inverses. They have been actively studied in category theory, homotopy theory, and algebraic \(K\)-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 \(K\)-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.