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101 0 $aeng
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181   $2rdacontent
182   $2rdamedia
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200 10$aMonoidal Categories and Topological Field Theory  /$fby Vladimir Turaev, Alexis Virelizier
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2017.
215   $a1 online resource (523 pages)
225 1 $aProgress in Mathematics,$x0743-1643 ;$v322
311   $a3-319-49833-9 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- 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.
330   $aThis monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research. Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphic to the Reshetikhin-Turaev surgery graph TQFT derived from the center of that category. The book is of interest to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads.
410  0$aProgress in Mathematics,$x0743-1643 ;$v322
606   $aCategory theory (Mathematics)
606   $aHomological algebra
606   $aManifolds (Mathematics)
606   $aComplex manifolds
606   $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035
606   $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027
615  0$aCategory theory (Mathematics).
615  0$aHomological algebra.
615  0$aManifolds (Mathematics).
615  0$aComplex manifolds.
615 14$aCategory Theory, Homological Algebra.
615 24$aManifolds and Cell Complexes (incl. Diff.Topology).
676   $a512.55
700   $aTuraev$b Vladimir$4aut$4http://id.loc.gov/vocabulary/relators/aut$067205
702   $aVirelizier$b Alexis$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254282003321
996   $aMonoidal Categories and Topological Field Theory$92124863
997   $aUNINA