3 citations · 3 across the 4 of their papers we have counts for
8 papers · 1 filter
Bimodule herds
Tomasz Brzezinski, Joost Vercruysse
The notion of a bimodule herd is introduced and studied. A bimodule herd consists of a - bimodule, its formal dual, called a pen, and a map, called a shepherd, which satisfie…
Quasi-co-Frobenius corings as Galois comodules
Joost Vercruysse
We compare several quasi-Frobenius-type properties for corings that appeared recently in literature and provide several new characterizations for each of these properties. By apply…
Galois theory in bicategories
Jose Gomez-Torrecillas, Joost Vercruysse
We develop a Galois (descent) theory for comonads within the framework of bicategories. We give generalizations of Beck's theorem and the Joyal-Tierney theorem. Many examples are p…
Quasi-Frobenius functors. Applications
F. Castano Iglesias, C. Nastasescu, J. Vercruysse
We investigate functors between abelian categories having a left adjoint and a right adjoint that are \emph{similar} (these functors are called \emph{quasi-Frobenius functors}). We…
Comatrix Corings and Galois Comodules over Firm Rings
J. Gomez-Torrecillas, J. Vercruysse
We give a notion of a comatrix coring which embodies all former constructions and, what is more interesting, leads to the formulation of a notion of Galois coring and the statement…
Local units versus local projectivity. Dualisations: Corings with local structure maps
Joost Vercruysse
We unify and generalize different notions of local units and local projectivity. We investigate the connection between these properties by constructing elementary algebras from loc…