# Corings and Comodules

@inproceedings{Brzezinski2003CoringsAC, title={Corings and Comodules}, author={Tomasz Brzezinski and Robert Wisbauer}, year={2003} }

Preface Notations 1. Coalgebras and comodules 2. Bialgebras and hopf algebras 3. Corings and comodules 4. Corings and extensions of rings 5. Corings and entwining structures 6. Weak corings and entwining Appendix.

## 241 Citations

ON CORINGS AND COMODULES

- Mathematics
- 2003

It is shown that the categories of R-coalgebras for a commutative unital ring R and the category of A-corings for some R-algebra A as well as their respective categories of comodules are locally…

Frobenius functors for corings

- Mathematics
- 2004

We investigate Frobenius pairs between categories of comodules over rather general corings. We particularize to the case of the adjoint pair of functors associated to a morphism of corings over…

Comonads and Galois Corings

- MathematicsAppl. Categorical Struct.
- 2006

We investigate which aspects of recent developments on Galois corings and comodules admit a formulation in terms of comonads. The general theory is applied to the study of Galois comodules over…

Group Corings

- MathematicsAppl. Categorical Struct.
- 2008

Group corings are introduced, and functors between categories of comodules over group corings, and the relationship to graded modules over graded rings are studied, as well as Morita contexts associated to a group coring.

Adjoint and Frobenius Pairs of Functors for Corings

- Mathematics
- 2005

We investigate adjoint and Frobenius pairs between categories of comodules over rather general corings. We particularize to the case of the adjoint pair of functors associated to a morphism of…

Comodules over semiperfect corings

- Mathematics
- 2011

We discuss when the Rat functor associated to a coring satisfying the left $\alpha$-condition is exact. We study the category of comodules over a semiperfect coring. We characterize semiperfect…

SYMMETRY FOR COMODULE CATEGORIES

- Mathematics
- 2012

For coalgebras C over a field, we study when the categories of left C-comodules and of right C-comodules are symmetric categories, in the sense that there is a duality between the categories of…

Compatibility Condition between ring and coring

- Mathematics
- 2007

We introduce the notion of bi-monoid in general monoidal category generalizing by this the notion of bialgebra. In the case of bimodules over a noncommutative algebra, we obtain a compatibility…

Comatrix Corings and Galois Comodules over Firm Rings

- Mathematics
- 2005

We construct comatrix corings on bimodules without finiteness conditions by using firm rings. This leads to the formulion of a notion of Galois coring which plays a key role in the statement of a…

Morita contexts and Galois theory for weak Hopf comodulelike algebras

- Mathematics
- 2011

We investigate the Morita context and graded cases for weak group corings and derive some equivalent conditions for µ to be surjective. Furthermore, we develop Galois theory for weak group corings.…