  The notions of conformal Lie 2-algebras and conformal omni-Lie algebras are
introduced and studied. It is proved that the category of conformal Lie
2-algebras and the category of 2-term conformal $L_{\infty}$-algebras are
equivalent. We construct conformal Lie 2-algebras from conformal omni-Lie
algebras and Leibniz conformal algebras.
