Comonadas y coanillos de Galois
Abstract
Starting from a comonad G on a category A, and a functor L : B -> A with a right adjoint R : A -> B, we will give a parametrization of the functors K from B to the category of all G-coalgebras that factorize throughout L in terms of homomorphisms of comonads from LR to G. Next, we will see under which conditions one of these functors K admits a right adjoint D. We will characterize when D is full and faithful, and we will conclude our general results by characterizing when K establishes an equivalence between the category B and the category of G-coalgebras. Obviously, the functors characterized in this way are, a fortiori, comonadic but, in contrast with the approach of Beck's Theorem, the comonad G is here given beforehand, and each functor K corresponds to a ``representation'' of G. Beck's theorem deals with the situation where G = LR. We apply our general results to the case of corings over firm rings.
Cite
@article{arxiv.math/0603348,
title = {Comonadas y coanillos de Galois},
author = {J. Gomez-Torrecillas},
journal= {arXiv preprint arXiv:math/0603348},
year = {2007}
}
Comments
Spanish. An English version will be published in the future. Some of the results in the first version were already familiar for categoy-theorists. In this second version, we notice this, and those results are credited. However, our elementary proofs and statements could become useful for non specialists. Thus, we have preserved them. Also, a gap was found in Lemma 2.3, which has been corrected, together with some other minor innacuracies, in the revised version