A correspondence between racks and g-digroups

The aim of this paper is to establish a correspondence between the categories given by the structures of racks and g-digroups, by defining three functors, denoted similarly to those in the case of rack-groups, \(Conj: \mathbf {g-dig}\rightarrow {\textbf {Rack}}\) $Conj:\mathbf{g}-\mathbf{dig}\to \mathbf{Rack}$ , \(As: {\textbf {Rack}}\rightarrow \mathbf {g-dig}\) $As:\mathbf{Rack}\to \mathbf{g}-\mathbf{dig}$ , and \(Inn: {\textbf {Rack}}\rightarrow \mathbf {g-dig}\) $Inn:\mathbf{Rack}\to \mathbf{g}-\mathbf{dig}$ . Additionally, we establish certain properties of these functors and prove, as in the case of rack-groups, that the functor As is left adjoint to the functor Conj.