Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Galois comodules   Galois comodules of a coring are studied.
  The conditions for a simple comodule to be a Galois comodule are found. A
special class of Galois comodules termed principal comodules is introduced.
These are defined as Galois comodules that are projective over their comodule
endomorphism rings. A complete description of principal comodules in the case a
background ring is a field is found. In particular it is shown that a (finitely
generated and projective) right comodule of an $A$-coring $\mathcal C$ is
principal provided a lifting of the canonical map is a split epimorphism in the
category of left $\mathcal C$-comodules. This description is then used to
characterise principal extensions or non-commutative principal bundles.
Specifically, it is proven that, over a field, any entwining structure
consisting of an algebra $A$, a coseparable coalgebra $C$ and a bijective
entwining map $\psi$ together with a group-like element in $C$ give rise to a
principal extension provided the lifted canonical map is surjective. Induction
of Galois and principal comodules via morphisms of corings is described. A
connection between the relative injectivity of a Galois comodule and the
properties of the extension of endomorphism rings associated to this comodule
is revealed.

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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat