Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalences between categories of modules and categories of comodules   We show the close connection between appearingly different Galois theories
for comodules introduced recently in [J. G\'omez-Torrecillas and J. Vercruysse,
Comatrix corings and Galois Comodules over firm rings, arXiv:math.RA/0509106.]
and [R. Wisbauer, On Galois comodules (2004), to appear in Comm. Algebra.].
Furthermore we study equivalences between categories of comodules over a coring
and modules over a firm ring. We show that these equivalences are related to
Galois theory for comodules.

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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: adap-org