  Given a pure state transformation $\psi\mapsto\phi$ restricted to
entanglement-assisted local operations with classical communication, we
determine a lower bound for the dimension of a catalyst allowing that
transformation. Our bound is stated in terms of the generalised concurrence
monotones (the usual concurrence of two qubits is one such monotone). We
further provide tools for deriving further conditions upon catalysts of pure
state transformations.
