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 $(C,\Delta ,\u03f5)$ 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)