I've been asking questions on reflectors before and I hope you are not getting annoyed. Apologies if that's the case.
My question is the following: Are there reflectors to the forgetful functor $U: \mathbf{CMon} \to \mathbf{Mon}$ from commutative monoids to the general monoids?
I know they exist in rings and groups but I have trouble working it out for monoids. Any answer is very much appreciated, but one not referring to the adjoint functor theorem is preferred.