Homotopic Hopf-Galois extensions: foundations and examples

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dc.creatorHess, Kathryn
dc.date2009-02-19
dc.date2009-04-17
dc.date.accessioned2026-07-07T13:04:54Z
dc.date.available2026-07-07T13:04:54Z
dc.descriptionHopf-Galois extensions of rings generalize Galois extensions, with the coaction of a Hopf algebra replacing the action of a group. Galois extensions with respect to a group $G$ are the Hopf-Galois extensions with respect to the dual of the group algebra of $G$. Rognes recently defined an analogous notion of Hopf-Galois extensions in the category of structured ring spectra, motivated by the fundamental example of the unit map from the sphere spectrum to $MU$. This article introduces a theory of homotopic Hopf-Galois extensions in a monoidal category with compatible model category structure that generalizes the case of structured ring spectra. In particular, we provide explicit examples of homotopic Hopf-Galois extensions in various categories of interest to topologists, showing that, for example, a principal fibration of simplicial monoids is a homotopic Hopf-Galois extension in the category of simplicial sets. We also investigate the relation of homotopic Hopf-Galois extensions to descent.
dc.description41 pages; new approach to model category structure of comodule categories, not using duality; slight modification in definition of homotopic Hopf-Galois extension, in the spirit of categorification; expanded discussion of descent, in terms of comodules over co-rings
dc.identifierhttps://arxiv.org/abs/0902.3393
dc.identifierhttp://arxiv.org/abs/0902.3393
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227330
dc.subjectAlgebraic Topology
dc.subjectRings and Algebras
dc.subject16W30, 55U35 (Primary); 13B05, 55P43, 55U10, 57T05 (Secondary)
dc.titleHomotopic Hopf-Galois extensions: foundations and examples
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