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arXiv · 2107.10526

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

Niles Johnson·Donald Yau
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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.

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BibTeXRIS

Niles Johnson, Donald Yau. 2021-07-22. Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory. https://arxiv.org/abs/2107.10526

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