# ON CORINGS AND COMODULES

@inproceedings{Porst2003ONCA, title={ON CORINGS AND COMODULES}, author={Hans-E. Porst}, year={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 presentable.

## 240 Citations

### Fundamental Constructions for Coalgebras, Corings, and Comodules

- MathematicsAppl. Categorical Struct.
- 2008

The various categories of corings, coalgebras, and comodules are studied from a categorical perspective and new results concerning the existence of limits and of factorizations of morphisms are obtained.

### Some Remarks on Localization in Coalgebras

- Mathematics
- 2006

We analyze the geometry of the Ext-quiver of a coalgebra C in order to study the behavior of simple and injective C-comodules under the action of the functors associated to a localizing subcategory…

### 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…

### 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.

### COHOMOLOGY FOR BICOMODULES. SEPARABLE AND MASCHKE FUNCTORS.

- Mathematics
- 2006

We introduce the category of bicomodules for a comonad in a Grothendieck category whose underlying functor is right exact and preserves direct sums. We char- acterize comonads with a separable…

### Corings over rings with local units

- Mathematics, Chemistry
- 2005

We show that the bicategory whose 0‐cells are corings over rings with local units is bi‐equivalent to the bicategory of comonads in (right) unital modules whose underlying functors are right exact…

### 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…

### Comatrix Corings an Invertible Bimodules

- Mathematics
- 2005

We extend Masuoka’s Theorem [11] concerning the isomorphism between the group of invertible bimodules in a non-commutative ring extension and the group of automorphisms of the associated Sweedler’s…

## References

SHOWING 1-8 OF 8 REFERENCES

### Corings and Comodules

- Mathematics
- 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…

### Hopf algebras : an introduction

- Mathematics
- 2001

Algebras and coalgebras comodules special classes of coalgebras bialgebras and Hopf algrebras integrals actions and coactions finite dimensional Hopf algebras the category theory language C-groups…

### On varieties and covarieties in a category

- MathematicsMathematical Structures in Computer Science
- 2003

By dualising, the concept of coequation is arrived at such that covarieties, that is, coequationally specified classes of coalgebras with cofree objects, correspond precisely to comonadic categories.

### Lehrbuch der Algebra

- MathematicsNature
- 1896

A “Treatise on Algebra” is rarely found to fulfil the promise of its title. It is too often a mere collection of problems and examples, thrown together without much regard to order or method; such…

### Accessible categories : the foundations of categorical model theory

- Mathematics
- 1989

[F-S] D. Fremlin and S. Shelah, Pointwise compact and stable sets of measurable functions, manuscript, 1990. [G-G-M-S] N. Ghoussoub, G. Godefroy, B. Maurey, W. Schachermayer, Some topological and…

### Germany E-mail: porst@math.uni-bremen

- Germany E-mail: porst@math.uni-bremen