Classification of 2-term \(L_\infty \)-algebras

We classify all 2-term \(L_\infty \) $L_{\infty }$ -algebras up to isomorphism. We show that such \(L_\infty \) $L_{\infty }$ -algebras are classified by a Lie algebra, a vector space, a representation (all up to isomorphism) and a cohomology class of the corresponding Lie algebra cohomology.