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, $$Conj: \mathbf {g-dig}\rightarrow {\textbf {Rack}}$$ C o n j : g - dig → Rack , $$As: {\textbf {Rack}}\rightarrow \mathbf {g-dig}$$ A s : Rack → g - dig , and $$Inn: {\textbf {Rack}}\rightarrow \mathbf {g-dig}$$ I n n : Rack → g - 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 .