coseparable coring

Coseparability of corings is a dual notion to separability of rings? (where one requires that the multiplication map is split).

An AA-coring (C,Δ,ϵ)(C,\Delta,\epsilon) is coseparable if the comultiplication Δ:CC AC\Delta:C\to C\otimes_A C splits as a CC-CC-bicomodule morphism. In other words, there is a morphism of AA-AA-bimodules p:C ACCp: C\otimes_A C\to C such that

Δp=(C Ap)(Δ AC)=(p AC)(C AΔ)\Delta\circ p = (C \otimes_A p)\circ(\Delta\otimes_A C) = (p\otimes_A C)\circ(C\otimes_A\Delta)
pΔ=Cp\circ\Delta = C

where C=Id CC = \mathrm{Id}_C.

Last revised on July 2, 2009 at 20:42:45. See the history of this page for a list of all contributions to it.