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A classification theorem for normal extensions

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arxiv 1604.02604 v1 pith:G4WQRM4H submitted 2016-04-09 math.CT

Mathieu Duckerts-Antoine , Tomas Everaert This is my paper · ORCID
classification math.CT
keywords extensionsnormalfunctorgaloisprovetheoremclassclassification
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For a particular class of Galois structures, we prove that the normal extensions are precisely those extensions that are "locally" split epic and trivial, and we use this to prove a "Galois theorem" for normal extensions. Furthermore, we interpret the normalisation functor as a Kan extension of the trivialisation functor.

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    The paper gives a Hopf-formula description of π1(B) for cocommutative Hopf algebras and a 5-term exact sequence relating their first two homology Hopf algebras.

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