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.

arXiv commentThis 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

References in corpus (21)

• Non-Abelian Anyons and Topological Quantum Computation
• Operads, homotopy algebra and iterated integrals for double loop spaces
• Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox
• The Classification of Two-Dimensional Extended Topological Field Theories
• A short introduction to Fibonacci anyon models
• Set theory for category theory
• Homotopy limits and colimits and enriched homotopy theory
• Experimental Test of Quantum No-Hiding Theorem
• Operads in iterated monoidal categories
• Constructing symmetric monoidal bicategories functorially
• The Multiplication on BP
• Derived Koszul Duality and Involutions in the Algebraic K-Theory of Spaces
• Operads of Wiring Diagrams
• An Inverse K-Theory Functor
• Drinfeld center of enriched monoidal categories
• Demonstration of the No-Hiding Theorem on the 5 Qubit IBM Quantum Computer in a Category Theoretic Framework
• Infinity Operads and Monoidal Categories with Group Equivariance
• Bimonoidal Structure of Probability Monads
• Closed categories vs. closed multicategories
• Strictification of categories weakly enriched in symmetric monoidal categories
• A multiplicative comparison of Waldhausen and Segal K-theory