---

＜電子ブック＞
Monoidal Categories and Topological Field Theory / by Vladimir Turaev, Alexis Virelizier
(Progress in Mathematics. ISSN:2296505X ; 322)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Birkhäuser)
出版年	2017
本文言語	英語
大きさ	XII, 523 p : online resource
著者標目	*Turaev, Vladimir author Virelizier, Alexis author SpringerLink (Online service)
件　名	LCSH:Algebra, Homological LCSH:Manifolds (Mathematics) FREE:Category Theory, Homological Algebra FREE:Manifolds and Cell Complexes
一般注記	Introduction -- Part I: Monoidal Categories -- Part 2: Hopf Algebras and Monads -- Part 3: State Sum Topological Field Theory -- Part 4: Graph Topological Field Theory -- Appendices -- Bibliography -- Index This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research. Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphicto the Reshetikhin-Turaev surgery graph TQFT derived from the center of that category. The book is of interest to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads HTTP:URL=https://doi.org/10.1007/978-3-319-49834-8

 類似資料