03572nam 22005535 450 99646662850331620200701115724.03-319-98137-410.1007/978-3-319-98137-6(CKB)4100000007110773(DE-He213)978-3-319-98137-6(MiAaPQ)EBC6302348(PPN)232467420(EXLCZ)99410000000711077320181101d2018 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierHopf Algebras and Their Generalizations from a Category Theoretical Point of View[electronic resource] /by Gabriella Böhm1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XI, 165 p. 239 illus.)Lecture Notes in Mathematics,0075-8434 ;22263-319-98136-6 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.Lecture Notes in Mathematics,0075-8434 ;2226Category theory (Mathematics)Homological algebraAssociative ringsRings (Algebra)Category Theory, Homological Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11035Associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Category theory (Mathematics).Homological algebra.Associative rings.Rings (Algebra).Category Theory, Homological Algebra.Associative Rings and Algebras.512.55Böhm Gabriellaauthttp://id.loc.gov/vocabulary/relators/aut760813MiAaPQMiAaPQMiAaPQBOOK996466628503316Hopf algebras and their generalizations from a category theoretical point of view1539997UNISA