nLab
coseparable coring

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

An A-coring (C,Δ,ϵ) is coseparable if the comultiplication Δ:CC AC splits as a C-C-bicomodule morphism. In other words, there is a morphism of A-A-bimodules p:C ACC 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 C.

Revised on July 2, 2009 20:42:45 by Toby Bartels (71.104.230.172)