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

Abstract

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.

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

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