Loday's conjectural Leibniz homology theory for groups

Let $\mathbf{Grp}$ be the category of groups, let $\mathbf{Zinb}^c$ denote coZinbiel coalgebras, and let $\mathbf{Com}^c$ denote cocommutative coalgebras. For a group $G$, write $\mathrm{HL}_{\bullet}(G,\Bbbk)$ for its conjectural Leibniz homology and $\mathrm{H}_{\bullet}(G,\Bbbk)$ for its Eilenberg–MacLane homology. Loday's conjecture. There exists a Leibniz homology theory defined for groups, naturally endowed with a coZinbiel coalgebra structure, namely a functor

$$\mathrm{HL}_{\bullet}(-,\Bbbk): \mathbf{Grp} \to \mathbf{Zinb}^c.$$

It is related to usual group homology by a natural morphism of cocommutative algebras

$$\mathrm{HL}_{\bullet}(G,\Bbbk) \to \mathrm{H}_{\bullet}(G,\Bbbk).$$

Moreover, this Leibniz homology is the natural homology theory of mathematical objects called coquecigrues, whose groups naturally carry the relevant structure. The conjecture proposes a group-level analogue of Leibniz homology for Lie algebras; the supplied text gives no evidence that it has been resolved.