Comonadas y coanillos de Galois
Abstract
Description
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.
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
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