Conformal Lie 2-algebras and conformal omni-Lie algebras

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 $L_{\mathrm{\infty }}$-algebras are equivalent. We construct conformal Lie 2-algebras from conformal omni-Lie algebras and Leibniz conformal algebras.