LEADER 02805nam a2200385 i 4500 001 991003635329707536 006 m o d 007 cr cnu|||unuuu 008 190404s2018 sz ob 001 0 eng d 020 $a3319981374$q(electronic bk.) 020 $a9783319981376$q(electronic bk.) 020 $z9783319981369$q(print) 024 7 $a10.1007/978-3-319-98137-6$2doi 035 $ab14363756-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 0 $a512.55$223 084 $aAMS 16T05 084 $aAMS 16T10 100 1 $aBöhm, Gabriella$0760813 245 10$aHopf algebras and their generalizations from a category theoretical point of view$h[e-book] /$cGabriella Böhm 264 1$aCham, Switzerland :$bSpringer,$c2018 300 $a1 online resource (xi, 165 pages) :$billustrations 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2226 504 $aIncludes bibliographical references and index 520 $aThese lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending the range of applications. Since Sweedler's work in the 1960s, Hopf algebras have earned a noble place in the garden of mathematical structures. Their use is well accepted in fundamental areas such as algebraic geometry, representation theory, algebraic topology, and combinatorics. Now, similar to having moved from groups to groupoids, it is becoming clear that generalizations of Hopf algebras must also be considered. This book offers a unified description of Hopf algebras and their generalizations from a category theoretical point of view. The author applies the theory of liftings to Eilenberg-Moore categories to translate the axioms of each considered variant of a bialgebra (or Hopf algebra) to a bimonad (or Hopf monad) structure on a suitable functor. Covered structures include bialgebroids over arbitrary algebras, in particular weak bialgebras, and bimonoids in duoidal categories, such as bialgebras over commutative rings, semi-Hopf group algebras, small categories, and categories enriched in coalgebras 650 0$aHopf algebras 856 40$zAn electronic book accessible through the World Wide Web$uhttp://link.springer.com/10.1007/978-3-319-98137-6 907 $a.b14363756$b03-03-22$c04-04-19 912 $a991003635329707536 996 $aHopf algebras and their generalizations from a category theoretical point of view$91539997 997 $aUNISALENTO 998 $ale013$b04-04-19$cm$d@ $e-$feng$gsz $h0$i0