LEADER 03547nam  22005535  450 
001 9910300116903321
005 20200701115724.0
010   $a3-319-98137-4
024 7 $a10.1007/978-3-319-98137-6
035   $a(CKB)4100000007110773
035   $a(DE-He213)978-3-319-98137-6
035   $a(MiAaPQ)EBC6302348
035   $a(PPN)232467420
035   $a(EXLCZ)994100000007110773
100   $a20181101d2018      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aHopf Algebras and Their Generalizations from a Category Theoretical Point of View /$fby Gabriella Böhm
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (XI, 165 p. 239 illus.)
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2226
311   $a3-319-98136-6 
330   $aThese lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending the range of applications. Since Sweedler's work in the 1960s, Hopf algebras have earned a noble place in the garden of mathematical structures. Their use is well accepted in fundamental areas such as algebraic geometry, representation theory, algebraic topology, and combinatorics. Now, similar to having moved from groups to groupoids, it is becoming clear that generalizations of Hopf algebras must also be considered. This book offers a unified description of Hopf algebras and their generalizations from a category theoretical point of view. The author applies the theory of liftings to Eilenberg?Moore categories to translate the axioms of each considered variant of a bialgebra (or Hopf algebra) to a bimonad (or Hopf monad) structure on a suitable functor. Covered structures include bialgebroids over arbitrary algebras, in particular weak bialgebras, and bimonoids in duoidal categories, such as bialgebras over commutative rings, semi-Hopf group algebras, small categories, and categories enriched in coalgebras. Graduate students and researchers in algebra and category theory will find this book particularly useful. Including a wide range of illustrative examples, numerous exercises, and completely worked solutions, it is suitable for self-study.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2226
606   $aCategory theory (Mathematics)
606   $aHomological algebra
606   $aAssociative rings
606   $aRings (Algebra)
606   $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
615  0$aCategory theory (Mathematics).
615  0$aHomological algebra.
615  0$aAssociative rings.
615  0$aRings (Algebra).
615 14$aCategory Theory, Homological Algebra.
615 24$aAssociative Rings and Algebras.
676   $a512.55
700   $aBöhm$b Gabriella$4aut$4http://id.loc.gov/vocabulary/relators/aut$0760813
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300116903321
996   $aHopf algebras and their generalizations from a category theoretical point of view$91539997
997   $aUNINA