\begin{definition}[Definition:Quasigroup/Left Quasigroup]
Let $\struct {S, \circ}$ be a magma. 
$\struct {S, \circ}$ is a '''left quasigroup''' {{iff}}:
:for all $a \in S$, the left regular representation $\lambda_a$ is a permutation on $S$.
That is:
:$\forall a, b \in S: \exists ! x \in S: a \circ x = b$
\end{definition}