Editing Digroup (section)

==Definition==
A digroup is a set ''D'' with two [[binary operation]]s,  <math>\vdash</math> and <math>\dashv</math>, that satisfy the following laws (e.g., Ongay 2010):
*Associativity:
::<math>\vdash</math> and <math>\dashv</math> are associative,
::<math>(x \vdash y) \vdash z = (x \dashv y) \vdash z,</math>
::<math>x \dashv (y \dashv z) = x \dashv (y \vdash z),</math>
::<math>(x \vdash y) \dashv z = x \vdash (y \dashv z).</math>
*Bar units:  There is at least one '''bar unit''', an <math>e \in D</math>, such that for every <math> x \in D,</math>
::<math>e \vdash x = x \dashv e = x.</math>
:The set of bar units is called the '''halo''' of ''D''.
*Inverse:  For each bar unit ''e'', each <math> x \in D</math> has a unique ''e''-inverse, <math>x_e^{-1} \in D</math>, such that
::<math>x \vdash x_e^{-1} = x_e^{-1} \dashv x = e.</math>