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.

    cover: exchange factorization axiom EF1]

The cover picture shows the Exchange Factorization axiom EF1 for an En-monoidal category. Download three volumes

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