We prove that an operator system $\mathcal S$ is nuclear in the category of
operator systems if and only if there exist nets of unital completely positive
maps $\varphi_\lambda : \cl S \to M_{n_\lambda}$ and $\psi_\lambda :
M_{n_\lambda} \to \cl S$ such that $\psi_\lambda \circ \varphi_\lambda$
converges to ${\rm id}_{\cl S}$ in the point-norm topology. Our proof is
independent of the Choi-Effros-Kirchberg characterization of nuclear
$C^*$-algebras and yields this characterization as a corollary.