Scalar extension of bicoalgebroids

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dc.creatorBalint, Imre
dc.date2007-07-06
dc.date.accessioned2026-07-07T08:14:19Z
dc.date.available2026-07-07T08:14:19Z
dc.descriptionAfter recalling the definition of a bicoalgebroid, we define comodules and modules over a bicoalgebroid. We construct the monoidal category of comodules, and define Yetter--Drinfel'd modules over a bicoalgebroid. It is proved that the Yetter--Drinfel'd category is monoidal and pre--braided just as in the case of bialgebroids, and is embedded into the one--sided center of the comodule category. We proceed to define Braided Cocommutative Coalgebras (BCC) over a bicoalgebroid, and dualize the scalar extension construction of Brzezinski and Militaru [2] and Balint and Slachanyi [1], originally applied to bialgebras and bialgebroids, to bicoalgebroids. A few classical examples of this construction are given. Identifying the comodule category over a bicoalgebroid with the category of coalgebras of the associated comonad, we obtain a comonadic (weakened) version of Schauenburg's theorem. Finally, we take a look at the scalar extension and braided cocommutative coalgebras from a (co--)monadic point of view.
dc.description24 pages, to appear in Applied Categorical Structures, special issue 'Algebras and Coalgebras'
dc.identifierhttps://arxiv.org/abs/0707.0975
dc.identifierhttp://arxiv.org/abs/0707.0975
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133082
dc.subjectQuantum Algebra
dc.subjectCategory Theory
dc.subject16W30, 18D10, 18D35, 18C15
dc.titleScalar extension of bicoalgebroids
dc.typetext

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