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 $(C,\Delta,\epsilon)$ is **coseparable** if the comultiplication $\Delta:C\to C\otimes_A C$ splits as a $C$-$C$-bicomodule morphism. In other words, there is a morphism of $A$-$A$-bimodules $p: C\otimes_A C\to C$ such that

$\Delta\circ p = (C \otimes_A p)\circ(\Delta\otimes_A C)
= (p\otimes_A C)\circ(C\otimes_A\Delta)$

$p\circ\Delta = C$

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

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