An equivalence of categories for Lie color algebras

Let k be a field with char k = p > 0 and G an abelian group with a bicharacter lambda on G. For each p-(G, lambda)-Lie color algebra L over k the p-universal enveloping algebra u(L) is a G-graded Hopf algebra, i.e., a Hopf algebra in the category M-kG of kG-comodules. In this paper we describe a subcategory of M-kG which is equivalent to the category of the finite dimensional p-(G, lambda)-Lie color algebras over k.