Given a Hopf algebra $H$, a left $H$-comodule $V$, and a surjective comodule endomorphism $f: V \to V$. Can somebody give:
(i) a set of neccessary, or sufficient, or both neccessary and sufficient, conditions for $f$ to have zero kernel?
(ii) an example of such a comodule map with non-zero kernel?
Thanks in advance guys