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[null,"1.","Record Nr.",null,"UNINA9910254282003321"]
[null,null,"Autore",null,"Turaev Vladimir"]
[null,null,"Titolo",null,"Monoidal Categories and Topological Field Theory  / / by Vladimir Turaev, Alexis Virelizier"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017"]
[null,null,"ISBN",null,"3-319-49834-7"]
[null,null,"Edizione",null,"[1st ed. 2017.]"]
[null,null,"Descrizione fisica",null,"1 online resource (523 pages)"]
[null,null,"Collana",null,"Progress in Mathematics, , 0743-1643 ; ; 322"]
[null,null,"Disciplina",null,"512.55"]
[null,null,"Soggetti",null,"Categories (Mathematics)"]
[{"$nulls":4},"Algebra, Homological"]
[{"$nulls":4},"Manifolds (Mathematics)"]
[{"$nulls":4},"Complex manifolds"]
[{"$nulls":4},"Category Theory, Homological Algebra"]
[{"$nulls":4},"Manifolds and Cell Complexes (incl. Diff.Topology)"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Introduction -- Part I: Monoidal Categories -- Part 2: Hopf Algebras and Monads -- Part 3: State Sum Topological Field Theory -- Part 4: Graph Topological Field Theory -- Appendices -- Bibliography -- Index."]
[null,null,null,"Sommario/riassunto","This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research. Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphic to the Reshetikhin-Turaev surgery graph TQFT derived from the center of that category. The book is of interest "]
[{"$nulls":4},"to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads."]