Bimonoidal Categories, En-monoidal Categories, and Algebraic K-theory
This is a three-volume work. Volumes I and II are by Donald Yau, and Volume III is jointly written by the two of us.
Download three volumes (pdf, 7Mb).
Update 2022-03-18: More typos fixed; new content about internal hom for M1-modules. 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.