Name
Abstract | ||
|---|---|---|
After 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 Brzeziński and Militaru (J Algebra
251:279–294, 2002) and Bálint and Szlachányi (J Algebra 296:520–560, 2006), 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. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1007/s10485-007-9098-z | Applied Categorical Structures |
Keywords | Field | DocType |
Scalar extension,Bicoalgebroids,Comodules,Primary 16W30,Secondary 16S40,18C15,18D10 | Complete category,Closed monoidal category,Topology,Discrete mathematics,Monad (category theory),Enriched category,Monoidal category,Closed category,Algebra,Comodule,Symmetric monoidal category,Mathematics | Journal |
Volume | Issue | ISSN |
16 | 1-2 | 0927-2852 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Imre Bálint | 1 | 3 | 2.12 |