> catalyst [2] - "a substance that enables a chemical reaction to proceed at a usually faster rate or under different conditions (as at a lower temperature) than otherwise possible"

To split water into hydrogen and oxygen, you need to add energy. It's very well possible that a catalyst can make the process more efficient than simple electrolysis, it can't change the fundamental fact that energy needs to be added for the reaction to occur. A catalyst will decrease the required activation energy, but not the total energy balance.

When you say that the catalyst itself must be 're-energized' or replaced, it sounds like the catalyst is the source of energy. Maybe that's not correct, but then the question remains: where does the energy come from?