說明 
xi, 163 pages : illustrations ; 24 cm 

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unmediated n rdamedia 

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系列 
Lecture notes in mathematics, 00758434 ; 2226


Lecture notes in mathematics (SpringerVerlag) ; 2226. 00758434

附註 
Includes bibliographical references (pages 155159) and index 

Lifting to EilenbergMoore categories  (Hopf) bimonads  (Hopf) bialgebras  (Hopf) bialgebroids  Weak (Hopf) bialgebras  (Hopf) bimonoids in duoidal categories  Solutions to the exercises 

"These lecture notes provide a selfcontained 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 EilenbergMoore 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, semiHopf 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 selfstudy"Page 4 of cover 
主題 
Hopf algebras

