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Monoidal categories and topological field theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Monoidal categories and topological field theoryby Vladimir Turaev, Alexis Virelizier.
Author:	Turaev, Vladimir.
other author:	Virelizier, Alexis.
Published:	Cham :Springer International Publishing :2017.
Description:	xii, 523 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Categories (Mathematics)
Online resource:	http://dx.doi.org/10.1007/978-3-319-49834-8
ISBN:	9783319498348$q(electronic bk.)

Monoidal categories and topological field theory
Turaev, Vladimir.

Monoidal categories and topological field theory[electronic resource] /by Vladimir Turaev, Alexis Virelizier. - Cham :Springer International Publishing :2017. - xii, 523 p. :ill., digital ;24 cm. - Progress in mathematics,v.3220743-1643 ;. - Progress in mathematics ;v.295..

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 Muger 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.

ISBN: 9783319498348$q(electronic bk.)

Standard No.: 10.1007/978-3-319-49834-8doiSubjects--Topical Terms:

206297
Categories (Mathematics)

LC Class. No.: QA169

Dewey Class. No.: 512.62

Monoidal categories and topological field theory
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505 0 $a 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.
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