6 papers
Naturally full functors in nature
A. Ardizzoni, S. Caenepeel, C. Menini +1
We introduce and discuss the notion of naturally full functor. The definition is similar to the definition of separable functor: a naturally full functor is a functorial version of…
Maschke functors, semisimple functors and separable functors of the second kind. Applications
S. Caenepeel, G. Militaru
We introduce separable functors of the second kind (or -separable functors) and -Maschke functors. -separable functors are generalizations of separable functors. Various n…
Frobenius Functors of the second kind
S. Caenepeel, E. De Groot, G. Militaru
A pair of adjoint functors is called a Frobenius pair of the second type if is a left adjoint of for some category equivalences and . Frobenius ring extens…
Doi-Koppinen modules for quantum groupoids
Tomasz Brzezinski, Stefaan Caenepeel, Gigel Militaru
A definition of a Doi-Koppinen datum over a noncommutative algebra is proposed. The idea is to replace a bialgebra in a standard Doi-Koppinen datum with a bialgebroid. The correspo…
Bialgebroids, -bialgebras and duality
Tomasz Brzezinski, Gigel Militaru
An equivalence between Lu's bialgebroids, Xu's bialgebroids with an anchor and Takeuchi's -bialgebras is explicitly proven. A new class of examples of bialgebroids is c…
Frobenius and Mashke type Theorems for Doi-Hopf modules and entwined modules revisited: a unified approach
Tomasz Brzezinski, S. Caenepeel, G. Militaru +1
We study when induction functors (and their adjoints) between categories of Doi-Hopf modules and, more generally, entwined modules are separable, resp. Frobenius. We present a unif…