Monads and comonads on module categories
G Böhm, T Brzeziński, R Wisbauer - Journal of Algebra, 2009 - Elsevier
Let A be a ring and MA the category of right A-modules. It is well known in module theory
that any A-bimodule B is an A-ring if and only if the functor−⊗ AB: MA→ MA is a monad (or …
that any A-bimodule B is an A-ring if and only if the functor−⊗ AB: MA→ MA is a monad (or …
[PDF][PDF] Monads of effective descent type and comonadicity
B Mesablishvili - Theory Appl. Categ, 2006 - emis.icm.edu.pl
We show, for an arbitrary adjunction F⊢ U: B→ A with B Cauchy complete, that the functor F
is comonadic if and only if the monad T on A induced by the adjunction is of effective …
is comonadic if and only if the monad T on A induced by the adjunction is of effective …
On coprime modules and comodules
IE Wijayanti, R Wisbauer - Communications in Algebra, 2009 - Taylor & Francis
Many observations about coalgebras were inspired by comparable situations for algebras.
Despite the prominent role of prime algebras, the theory of a corresponding notion for …
Despite the prominent role of prime algebras, the theory of a corresponding notion for …
Galois corings from the descent theory point of view
S Caenepeel - arXiv preprint math/0311377, 2003 - arxiv.org
arXiv:math/0311377v1 [math.RA] 21 Nov 2003 Page 1 arXiv:math/0311377v1 [math.RA] 21
Nov 2003 Fields Institute Communications Volume 00, 0000 Galois corings from the …
Nov 2003 Fields Institute Communications Volume 00, 0000 Galois corings from the …
Galois-type extensions and equivariant projectivity
T Brzezinski, PM Hajac - arXiv preprint arXiv:0901.0141, 2009 - arxiv.org
The theory of general Galois-type extensions is presented, including the interrelations
between coalgebra extensions and algebra (co) extensions, properties of corresponding …
between coalgebra extensions and algebra (co) extensions, properties of corresponding …
Comonads and Galois corings
J Gómez-Torrecillas - Applied Categorical Structures, 2006 - Springer
Comonads and Galois Corings Page 1 Appl Categor Struct (2006) 14:579–598 DOI 10.1007/s10485-006-9049-0
Comonads and Galois Corings J. Gómez-Torrecillas Received: 7 March 2006 / Accepted …
Comonads and Galois Corings J. Gómez-Torrecillas Received: 7 March 2006 / Accepted …
Galois theory for comatrix corings: descent theory, Morita theory, Frobenius and separability properties
S Caenepeel, E De Groot, J Vercruysse - Transactions of the American …, 2007 - ams.org
El Kaoutit and Gómez-Torrecillas introduced comatrix corings, generalizing Sweedler's
canonical coring, and proved a new version of the Faithfully Flat Descent Theorem. They …
canonical coring, and proved a new version of the Faithfully Flat Descent Theorem. They …
[HTML][HTML] Semiseparable functors
A Ardizzoni, L Bottegoni - Journal of Algebra, 2024 - Elsevier
In this paper we introduce and investigate the notion of semiseparable functor. One of its first
features is that it allows a novel description of separable and naturally full functors in terms …
features is that it allows a novel description of separable and naturally full functors in terms …
Morita theory for Hopf algebroids, principal bibundles, and weak equivalences
L El Kaoutit, N Kowalzig - Documenta Mathematica, 2017 - ems.press
We show that two flat commutative Hopf algebroids are Morita equivalent if and only if they
are weakly equivalent and if and only if there exists a principal bibundle connecting them …
are weakly equivalent and if and only if there exists a principal bibundle connecting them …
Local units versus local projectivity dualisations: Corings with local structure maps
J Vercruysse - Communications in Algebra®, 2006 - Taylor & Francis
We unify and generalize different notions of local units and local projectivity. We investigate
the connection between these properties by constructing elementary algebras from locally …
the connection between these properties by constructing elementary algebras from locally …