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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 Chapters three through five feature previously unpublished results on coherence and strictification of involutive categories and involutive monoidal categories, showcasing the author's state-of-the-art research.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.
List of contents
Category Theory.- Involutive Categories.- Coherence of Involutive Categories.- Involutive Monoidal Categories.- Coherence of Involutive Monoidal Categories.- Coherence of Involutive Symmetric Monoidal Categories.- Categorical Gelfand-Naimark-Segal Construction.- Involutive Operads.
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.
Report
"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)
