Involutive Category Theory
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Beschreibung
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 Chapters three through five feature previously unpublished results on coherence and strictification of involutive categories and involutive monoidal categories, showcasing the author’s state-of-the-art research.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.
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 Chapters three through five feature previously unpublished results on coherence and strictification of involutive categories and involutive monoidal categories, showcasing the author’s state-of-the-art research.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.
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
Autor*in
Donald Yau
Themen in »Involutive Category Theory«
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
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“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)
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