We show that a Banach space X is an ℒ₁-space (respectively, an ${ℒ}_{\infty }$-space) if and only if it has the lifting (respectively, the extension) property for polynomials which are weakly continuous on bounded sets. We also prove that X is an ℒ₁-space if and only if the space ${}_{wb}{(}^{m}X)$ of m-homogeneous scalar-valued polynomials on X which are weakly continuous on bounded sets is an ${ℒ}_{\infty }$-space.