{"product_id":"9783319498331","title":"Progress in Mathematics","description":"\u003ch1\u003eProgress in Mathematics\u003c\/h1\u003e \u003ch2\u003eTuraev, Vladimir; Virelizier, Alexis\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003ePart 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 isomorphic tothe Reshetikhin-Turaev surgery graph TQFT derived from the center of that category.\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe book is of interest to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2017-07-07\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9783319498331\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-319-49834-8\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 523\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":46541461454988,"sku":"9783319498331","price":179.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783319498331.jpg?v=1775736591","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783319498331","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}