The Resource Monoidal Categories and Topological Field Theory, by Vladimir Turaev, Alexis Virelizier, (electronic resource)

Monoidal Categories and Topological Field Theory, by Vladimir Turaev, Alexis Virelizier, (electronic resource)

Label
Monoidal Categories and Topological Field Theory
Title
Monoidal Categories and Topological Field Theory
Statement of responsibility
by Vladimir Turaev, Alexis Virelizier
Creator
Contributor
Author
Author
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Turaev, Vladimir
Dewey number
512.55
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • SsNAyoqqN7U
  • XaeKjNOmZIg
LC call number
QA169
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Virelizier, Alexis.
Series statement
Progress in Mathematics,
Series volume
322
http://library.link/vocab/subjectName
  • Algebra
  • Cell aggregation
  • Category Theory, Homological Algebra
  • Manifolds and Cell Complexes (incl. Diff.Topology)
Label
Monoidal Categories and Topological Field Theory, by Vladimir Turaev, Alexis Virelizier, (electronic resource)
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Edition
1st ed. 2017.
Extent
1 online resource (523 pages).
Form of item
online
Isbn
9783319498348
Media category
computer
Media MARC source
rdamedia
Other control number
10.1007/978-3-319-49834-8
Sound
unknown sound
Specific material designation
remote
System control number
  • (CKB)3710000001418423
  • (MiAaPQ)EBC4890742
  • (DE-He213)978-3-319-49834-8
  • (EXLCZ)993710000001418423
Label
Monoidal Categories and Topological Field Theory, by Vladimir Turaev, Alexis Virelizier, (electronic resource)
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Edition
1st ed. 2017.
Extent
1 online resource (523 pages).
Form of item
online
Isbn
9783319498348
Media category
computer
Media MARC source
rdamedia
Other control number
10.1007/978-3-319-49834-8
Sound
unknown sound
Specific material designation
remote
System control number
  • (CKB)3710000001418423
  • (MiAaPQ)EBC4890742
  • (DE-He213)978-3-319-49834-8
  • (EXLCZ)993710000001418423

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