Omni-Lie Color Algebras and Lie Color 2-Algebras

Omni-Lie color algebras over an abelian group with a bicharacter are studied. The notions of 2-term color $L_{\infty}$-algebras and Lie color 2-algebras are introduced. It is proved that there is a one-to-one correspondence between Lie color 2-algebras and 2-term color $L_{\infty}$-algebras.