• Corpus ID: 2971491

# 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

• H. Porst
• Mathematics
Appl. 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

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

### Purity and homotopy theory of coalgebras

• M. Stelzer
• Mathematics
Journal of Pure and Applied Algebra
• 2019

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

• Mathematics
Appl. 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

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

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