Given a -coalgebra-Galois extension of a -algebra , which is the appropriate generalization of a Hopf-Galois extension, where is faithfully flat over the base as a left -module, one constructs a coring, Ehresmann coring, out of these data. Its role is somewhat analogous to the gauge groupoid (see Atiyah Lie groupoid), and in Hopf-Galois case it is an intermediate stage in constructing another analogue, (Ehresmann-)Schauenburg bialgebroid, see there. Definition A right -coalgebra-Galois extension is a -algebra together with a right -coaction where is the subalgebra of coinvariants if the map is bijective. The map , is the translation map: The underlying bimodule of the Ehresmann coring is the subbimodule If is faithfully flat as a left -module then is a -coring via and comultiplication given by multiplication: . Literature T. Brzeziński, R. Wisbauer, Corings and comodules, London Math. Soc. Lec. Note Series 309, Cambridge 2003. Last revised on August 20, 2026 at 13:41:02. See the history of this page for a list of all contributions to it.