Matches in SemOpenAlex for { <https://semopenalex.org/work/W2165527471> ?p ?o ?g. }
Showing items 1 to 91 of
91
with 100 items per page.
- W2165527471 endingPage "800" @default.
- W2165527471 startingPage "745" @default.
- W2165527471 abstract "We define Hopf monads on an arbitrary monoidal category, extending the definition given in Bruguières and Virelizier (2007) [5] for monoidal categories with duals. A Hopf monad is a bimonad (or opmonoidal monad) whose fusion operators are invertible. This definition can be formulated in terms of Hopf adjunctions, which are comonoidal adjunctions with an invertibility condition. On a monoidal category with internal Homs, a Hopf monad is a bimonad admitting a left and a right antipode. Hopf monads generalize Hopf algebras to the non-braided setting. They also generalize Hopf algebroids (which are linear Hopf monads on a category of bimodules admitting a right adjoint). We show that any finite tensor category is the category of finite-dimensional modules over a Hopf algebroid. Any Hopf algebra in the center of a monoidal category C gives rise to a Hopf monad on C. The Hopf monads so obtained are exactly the augmented Hopf monads. More generally if a Hopf monad T is a retract of a Hopf monad P, then P is a cross product of T by a Hopf algebra of the center of the category of T-modules (generalizing the Radford–Majid bosonization of Hopf algebras). We show that the comonoidal comonad of a Hopf adjunction is canonically represented by a cocommutative central coalgebra. As a corollary, we obtain an extension of Sweedlerʼs Hopf module decomposition theorem to Hopf monads (in fact to the weaker notion of pre-Hopf monad)." @default.
- W2165527471 created "2016-06-24" @default.
- W2165527471 creator A5060553119 @default.
- W2165527471 creator A5064622353 @default.
- W2165527471 creator A5073756839 @default.
- W2165527471 date "2011-06-01" @default.
- W2165527471 modified "2023-10-03" @default.
- W2165527471 title "Hopf monads on monoidal categories" @default.
- W2165527471 cites W1515443984 @default.
- W2165527471 cites W1975166962 @default.
- W2165527471 cites W2001058510 @default.
- W2165527471 cites W2019048170 @default.
- W2165527471 cites W2048649562 @default.
- W2165527471 cites W2048894573 @default.
- W2165527471 cites W2090111875 @default.
- W2165527471 cites W2963128908 @default.
- W2165527471 cites W4210278276 @default.
- W2165527471 doi "https://doi.org/10.1016/j.aim.2011.02.008" @default.
- W2165527471 hasPublicationYear "2011" @default.
- W2165527471 type Work @default.
- W2165527471 sameAs 2165527471 @default.
- W2165527471 citedByCount "104" @default.
- W2165527471 countsByYear W21655274712012 @default.
- W2165527471 countsByYear W21655274712013 @default.
- W2165527471 countsByYear W21655274712014 @default.
- W2165527471 countsByYear W21655274712015 @default.
- W2165527471 countsByYear W21655274712016 @default.
- W2165527471 countsByYear W21655274712017 @default.
- W2165527471 countsByYear W21655274712018 @default.
- W2165527471 countsByYear W21655274712019 @default.
- W2165527471 countsByYear W21655274712020 @default.
- W2165527471 countsByYear W21655274712021 @default.
- W2165527471 countsByYear W21655274712022 @default.
- W2165527471 countsByYear W21655274712023 @default.
- W2165527471 crossrefType "journal-article" @default.
- W2165527471 hasAuthorship W2165527471A5060553119 @default.
- W2165527471 hasAuthorship W2165527471A5064622353 @default.
- W2165527471 hasAuthorship W2165527471A5073756839 @default.
- W2165527471 hasBestOaLocation W21655274711 @default.
- W2165527471 hasConcept C130856480 @default.
- W2165527471 hasConcept C136119220 @default.
- W2165527471 hasConcept C138354692 @default.
- W2165527471 hasConcept C148647251 @default.
- W2165527471 hasConcept C156772000 @default.
- W2165527471 hasConcept C202444582 @default.
- W2165527471 hasConcept C2778249326 @default.
- W2165527471 hasConcept C2779904274 @default.
- W2165527471 hasConcept C29712632 @default.
- W2165527471 hasConcept C33923547 @default.
- W2165527471 hasConcept C33959348 @default.
- W2165527471 hasConcept C55192134 @default.
- W2165527471 hasConcept C67996461 @default.
- W2165527471 hasConcept C98912367 @default.
- W2165527471 hasConceptScore W2165527471C130856480 @default.
- W2165527471 hasConceptScore W2165527471C136119220 @default.
- W2165527471 hasConceptScore W2165527471C138354692 @default.
- W2165527471 hasConceptScore W2165527471C148647251 @default.
- W2165527471 hasConceptScore W2165527471C156772000 @default.
- W2165527471 hasConceptScore W2165527471C202444582 @default.
- W2165527471 hasConceptScore W2165527471C2778249326 @default.
- W2165527471 hasConceptScore W2165527471C2779904274 @default.
- W2165527471 hasConceptScore W2165527471C29712632 @default.
- W2165527471 hasConceptScore W2165527471C33923547 @default.
- W2165527471 hasConceptScore W2165527471C33959348 @default.
- W2165527471 hasConceptScore W2165527471C55192134 @default.
- W2165527471 hasConceptScore W2165527471C67996461 @default.
- W2165527471 hasConceptScore W2165527471C98912367 @default.
- W2165527471 hasIssue "2" @default.
- W2165527471 hasLocation W21655274711 @default.
- W2165527471 hasLocation W21655274712 @default.
- W2165527471 hasLocation W21655274713 @default.
- W2165527471 hasLocation W21655274714 @default.
- W2165527471 hasOpenAccess W2165527471 @default.
- W2165527471 hasPrimaryLocation W21655274711 @default.
- W2165527471 hasRelatedWork W1976358737 @default.
- W2165527471 hasRelatedWork W2077337146 @default.
- W2165527471 hasRelatedWork W2165527471 @default.
- W2165527471 hasRelatedWork W2172203798 @default.
- W2165527471 hasRelatedWork W2373478153 @default.
- W2165527471 hasRelatedWork W2899415153 @default.
- W2165527471 hasRelatedWork W2951002534 @default.
- W2165527471 hasRelatedWork W2953230674 @default.
- W2165527471 hasRelatedWork W3026822304 @default.
- W2165527471 hasRelatedWork W4297907846 @default.
- W2165527471 hasVolume "227" @default.
- W2165527471 isParatext "false" @default.
- W2165527471 isRetracted "false" @default.
- W2165527471 magId "2165527471" @default.
- W2165527471 workType "article" @default.