  Given a symmetric operad $P$, and a signature (or generating sequence) $\Phi$
for $P$, we define a notion of the "categorification" (or "weakening") of $P$
with respect to $\Phi$. When $P$ is the symmetric operad whose algebras are
commutative monoids, with the standard signature, we recover the notion of
symmetric monoidal categories. We then show that this categorification is
independent (up to equivalence) of the choice of signature.
