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Infinite Comatrix Corings

L. El Kaoutit·J. Gomez-Torrecillas
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Abstract

We characterize the corings whose category of comodules has a generating set of small projective comodules in terms of the (non commutative) descent theory. In order to extricate the structure of these corings, we give a generalization of the notions of comatrix coring and Galois comodule which avoid finiteness conditions. A sufficient condition for a coring to be isomorphic to an infinite comatrix coring is found. We deduce in particular that any coalgebra over a field and the coring associated to a group-graded ring are isomorphic to adequate infinite comatrix corings. We also characterize when the free module canonically associated to a (not necessarily finite) set of group like elements is Galois.

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L. El Kaoutit, J. Gomez-Torrecillas. 2004-03-15. Infinite Comatrix Corings. https://arxiv.org/abs/math/0403249

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