Infinity Operads And Monoidal Categories With Group Equivariance - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Infinity Operads And Monoidal Categories With Group Equivariance write by Donald Yau. This book was released on 2021-12-02. Infinity Operads And Monoidal Categories With Group Equivariance available in PDF, EPUB and Kindle. This monograph provides a coherent development of operads, infinity operads, and monoidal categories, equipped with equivariant structures encoded by an action operad. A group operad is a planar operad with an action operad equivariant structure. In the first three parts of this monograph, we establish a foundation for group operads and for their higher coherent analogues called infinity group operads. Examples include planar, symmetric, braided, ribbon, and cactus operads, and their infinity analogues. For example, with the tools developed here, we observe that the coherent ribbon nerve of the universal cover of the framed little 2-disc operad is an infinity ribbon operad.In Part 4 we define general monoidal categories equipped with an action operad equivariant structure and provide a unifying treatment of coherence and strictification for them. Examples of such monoidal categories include symmetric, braided, ribbon, and coboundary monoidal categories, which naturally arise in the representation theory of quantum groups and of coboundary Hopf algebras and in the theory of crystals of finite dimensional complex reductive Lie algebras.
Infinity Operads And Monoidal Categories With Group Equivariance
Infinity Operads And Monoidal Categories With Group Equivariance - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Infinity Operads And Monoidal Categories With Group Equivariance write by Donald Yau. This book was released on 2021. Infinity Operads And Monoidal Categories With Group Equivariance available in PDF, EPUB and Kindle. "This monograph provides a coherent development of operads, infinity operads, and monoidal categories, equipped with equivariant structures encoded by an action operad. A group operad is a planar operad with an action operad equivariant structure. In the first three parts of this monograph, we establish a foundation for group operads and for their higher coherent analogues called infinity group operads. Examples include planar, symmetric, braided, ribbon, and cactus operads, and their infinity analogues. For example, with the tools developed here, we observe that the coherent ribbon nerve of the universal cover of the framed little 2-disc operad is an infinity ribbon operad. In Part 4 we define general monoidal categories equipped with an action operad equivariant structure and provide a unifying treatment of coherence and strictification for them. Examples of such monoidal categories include symmetric, braided, ribbon, and coboundary monoidal categories, which naturally arise in the representation theory of quantum groups and of coboundary Hopf algebras and in the theory of crystals of finite dimensional complex reductive Lie algebras"--
Grothendieck Construction of Bipermutative-Indexed Categories
Grothendieck Construction of Bipermutative-Indexed Categories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Grothendieck Construction of Bipermutative-Indexed Categories write by Donald Yau. This book was released on 2023-12-06. Grothendieck Construction of Bipermutative-Indexed Categories available in PDF, EPUB and Kindle. This monograph is the first and only book-length reference for this material. Contents of Chapter 2, Chapter 3, Part 2, and Part 3 is new, not having appeared in any of the research literature. The book will appeal to mathematicians interested in topology. Book shelved as a reference title.
String-Net Construction of RCFT Correlators
String-Net Construction of RCFT Correlators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook String-Net Construction of RCFT Correlators write by Jürgen Fuchs. This book was released on 2023-01-01. String-Net Construction of RCFT Correlators available in PDF, EPUB and Kindle. This book studies using string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. The authors obtain concise geometric expressions for the objects describing bulk and boundary fields in terms of idempotents in the cylinder category of the underlying modular fusion category, comprising more general classes of fields than is standard in the literature. Combining these idempotents with Frobenius graphs on the world sheet yields string nets that form a consistent system of correlators, i.e. a system of invariants under appropriate mapping class groups that are compatible with factorization. The authors extract operator products of field objects from specific correlators; the resulting operator products are natural algebraic expressions that make sense beyond semisimplicity. They also derive an Eckmann-Hilton relation internal to a braided category, thereby demonstrating the utility of string nets for understanding algebra in braided tensor categories. Finally, they introduce the notion of a universal correlator. This systematizes the treatment of situations in which different world sheets have the same correlator and allows for the definition of a more comprehensive mapping class group.
Involutive Category Theory
Involutive Category Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Involutive Category Theory write by Donald Yau. This book was released on 2020-11-30. Involutive Category Theory available in PDF, EPUB and Kindle. 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.
