03587nam 22005895 450 991025428200332120200703010917.03-319-49834-710.1007/978-3-319-49834-8(CKB)3710000001418423(MiAaPQ)EBC4890742(DE-He213)978-3-319-49834-8(PPN)202991466(EXLCZ)99371000000141842320170628d2017 u| 0engurcnu||||||||rdacontentrdamediardacarrierMonoidal Categories and Topological Field Theory /by Vladimir Turaev, Alexis Virelizier1st ed. 2017.Cham :Springer International Publishing :Imprint: Birkhäuser,2017.1 online resource (523 pages)Progress in Mathematics,0743-1643 ;3223-319-49833-9 Includes bibliographical references and index.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 isomorphic to 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.Progress in Mathematics,0743-1643 ;322Category theory (Mathematics)Homological algebraManifolds (Mathematics)Complex manifoldsCategory Theory, Homological Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11035Manifolds and Cell Complexes (incl. Diff.Topology)https://scigraph.springernature.com/ontologies/product-market-codes/M28027Category theory (Mathematics).Homological algebra.Manifolds (Mathematics).Complex manifolds.Category Theory, Homological Algebra.Manifolds and Cell Complexes (incl. Diff.Topology).512.55Turaev Vladimirauthttp://id.loc.gov/vocabulary/relators/aut67205Virelizier Alexisauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910254282003321Monoidal Categories and Topological Field Theory2124863UNINA