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Quantum Physics and LinguisticsA Compositional, Diagrammatic Discourse$
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Chris Heunen, Mehrnoosh Sadrzadeh, and Edward Grefenstette

Print publication date: 2013

Print ISBN-13: 9780199646296

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199646296.001.0001

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Hopf Algebras—Variant Notions and Reconstruction Theorems

Hopf Algebras—Variant Notions and Reconstruction Theorems

Chapter:
(p.115) chapter-5 Hopf Algebras—Variant Notions and Reconstruction Theorems
Source:
Quantum Physics and Linguistics
Author(s):

Joost Vercruysse

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199646296.003.0005

Hopf algebras are closely related to monoidal categories. More precisely, k-Hopf algebras can be characterized as those algebras whose category of finite-dimensional representations is an autonomous monoidal category such that the forgetful functor to k-vectorspaces is a strict monoidal functor. This result is known as the Tannaka reconstruction theorem (for Hopf algebras). Because of the importance of both Hopf algebras in various fields, over the last few decades, many generalizations have been defined. We will survey these different generalizations from the point of view of the Tannaka reconstruction theorem.

Keywords:   Hopf algebras, autonomous monoidal categories, vector spaces, Tannaka reconstruction theorem

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