Scalar extension of bicoalgebroids. (English) Zbl 1151.16037
Bicoalgebroids were introduced by Brzeziński and Militaru as the structure that dualizes bialgebroids in the sense of reversing arrows. In the paper under review the author introduces the concepts of comodules, modules and Yetter-Drinfel’d modules over a bicoalgebroid. The monoidal category of comodules is constructed. It is proved that the Yetter-Drinfel’d category is monoidal and pre-braided, which can be embedded into the one-sided center of the comodule category. Braided cocommutative coalgebras over a bicoalgebroid are also studied and some classical examples of this construction are given. A comonadic (weakened) version of Schauenburg’s theorem is also obtained.
Reviewer: Yang Shilin (Beijing)
MSC:
| 16W30 | Hopf algebras (associative rings and algebras) (MSC2000) |
| 18D10 | Monoidal, symmetric monoidal and braided categories (MSC2010) |
| 16S40 | Smash products of general Hopf actions |
Keywords:
scalar extensions; bicoalgebroids; comodules; Yetter-Drinfeld modules; Yetter-Drinfeld categoriesReferences:
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