On the conjectural Leibniz cohomology for groups

This article presents results which are consistent with conjectures about Leibniz (co)homology for discrete groups, due to J. L. Loday in 2003. We prove that rack cohomology has properties very close to the properties expected for the conjectural Leibniz cohomology. In particular, we prove the existence of a graded dendriform algebra structure on rack cohomology, and we construct a graded associative algebra morphism H •(−) → HR •(−) from group cohomology to rack cohomology which is injective for ● = 1.