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Field name	Details
Dewey Class	512.6 (DDC 23)
Title	Hopf Algebras and Their Generalizations from a Category Theoretical Point of View ([Ebook]) / by Gabriella Böhm
Author	Böhm, Gabriella
Publication	Cham : Springer International Publishing , 2018
Physical Details	1 online resource (XI, 165 pages)
Series	Lecture Notes in Mathematics ; 2226
ISBN	9783319981376
Summary Note	These lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending the range of applications.Since Sweedler's work in the 1960s, Hopf algebras have earned a noble place in the garden of mathematical structures. Their use is well accepted in fundamental areas such as algebraic geometry, representation theory, algebraic topology, and combinatorics. Now, similar to having moved from groups to groupoids, it is becoming clear that generalizations of Hopf algebras must also be considered. This book offers a unified description of Hopf algebras and their generalizations from a category theoretical point of view. The author applies the theory of liftings to Eilenberg–Moore categories to translate the axioms of each considered variant of a bialgebra (or Hopf algebra) to a bimonad (or Hopf monad) structure on a suitable functor. Covered structures include bialgebroids over arbitrary algebras, in particular weak bialgebras, and bimonoids in duoidal categories, such as bialgebras over commutative rings, semi-Hopf group algebras, small categories, and categories enriched in coalgebras.Graduate students and researchers in algebra and category theory will find this book particularly useful. Including a wide range of illustrative examples, numerous exercises, and completely worked solutions, it is suitable for self-study.:
Mode of acces to digital resource	Digital book. Cham Springer International Publishing 2018. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
System details note	Online access to this digital book is restricted to subscribing institutions through IP address (only for SISSA internal users)
Internet Site	https://doi.org/10.1007/978-3-319-98137-6
Links to Related Works	Subject References: Algebra . Associative Rings and Algebras . Category Theory . Homological algebra . Authors: Böhm, Gabriella . Series: Lecture Notes in Mathematics . Classification: 512.6 (DDC 23) .

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Hopf Algebras and Their Generalizations from a Category Theoretical Point of View

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