Adjoint and Frobenius Pairs of Functors for Corings

Abstract

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 corings over different base rings, which leads to a reasonable notion of Frobenius coring extension. When applied to corings stemming from entwining structures, we obtain new results in this setting and in graded ring theory.

ACKNOWLEDGMENTS

I would like to thank my advisor, Professor José Gómez-Torrecillas, for his assistance in the writing of this article, and for interesting discussions.

I would also like to express my deep gratitude to Professor Edgar Enochs for communicating the example of a commutative self-injective ring which is not coherent, and to Professor Tomasz Brzeziński for his assistance, for his careful reading of this article, and for his useful comments.

Finally, I wish to thank Editor Robert Wisbauer and the referee for some helpful suggestions.

Notes

Communicated by R. Wisbauer.