Overview
- Offers an accessible introduction to involutive categories and involutive operads, bringing readers from the basics to cutting-edge research
- Collects and expands upon material that has previously been spread across the literature
- Serves as an ideal resource for independent study with detailed exercises appearing at the end of each chapter
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2279)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
This monograph introduces involutive categories and involutive operads, featuring applications to the GNS construction and algebraic quantum field theory. The author adopts an accessible approach for readers seeking an overview of involutive category theory, from the basics to cutting-edge applications. Additionally, the author’s own recent advances in the area are featured, never having appeared previously in the literature.
The opening chapters offer an introduction to basic category theory, ideal for readers new to the area. Chapters three through five feature previously unpublished results on coherence and strictification of involutive categories and involutive monoidal categories, showcasing the author’s state-of-the-art research. Chapters on coherence of involutive symmetric monoidal categories, and categorical GNS construction follow. The last chapter covers involutive operads and lays important coherence foundations for applications to algebraic quantum field theory.
With detailed explanations and exercises throughout, Involutive Category Theory is suitable for graduate seminars and independent study. Mathematicians and mathematical physicists who use involutive objects will also find this a valuable reference.
Similar content being viewed by others
Keywords
- Involutive categories
- Involutive monoidal categories
- Involutive monoids
- Involutive monads
- Involutive operads
- Involutive operator
- Strictification
- Strictification monoidal category
- GNS construction
- GNS construction physics
- Gelfand Naimark Segal construction
- Gelfand Naimark Segal theorem
- Algebraic quantum field theory
- Involutive structures
- Complex unital star-algebras
- Involutive functors
Table of contents (8 chapters)
-
Front Matter
-
Back Matter
Reviews
“This is the first book whose central topic is involutive categories. It is written at the first year graduate level and is pretty much self-contained. It contains exercises and notes at the end of every chapter. It may be a useful reference for mathematicians and physicists working with involutive objects.” (Bojana Femic, Mathematical Reviews, May, 2022)
Authors and Affiliations
About the author
Donald Yau is Professor of Mathematics at The Ohio State University at Newark. He obtained his PhD at MIT and held a post-doctoral position at the University of Illinois at Urbana-Champaign. His research focuses on algebraic topology. He has authored over forty articles and eight books, including the Springer titles Operads of Wiring Diagrams and Infinity Properads and Infinity Wheeled Properads.
Bibliographic Information
Book Title: Involutive Category Theory
Authors: Donald Yau
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-61203-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-61202-3Published: 01 December 2020
eBook ISBN: 978-3-030-61203-0Published: 30 November 2020
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 243
Number of Illustrations: 197 b/w illustrations