A homogeneous catalyst is a catalyst which is in the same phase as the reactant. For example, the catalyst is in aqueous solution, and the reactants are in the same aqueous solution.
Catalysts work by changing oxidation state
In a catalysed reaction, BOTH the steps will have a lower activation energy than the uncatalysed reaction. So this reaction pathway is faster.
Autocatalysis is the name given to a reaction in which a product is the catalyst.
Regeneration is a key step in all catalytic reactions.
An example of a autocatalytic species is Mn2+ that is produced in the reaction between C2O42- ions and MnO4- ions.