\begin{definition}[Definition:Semigroup with respect to Equivalence Relation]
Let $C$ be a class.
Let $\thickapprox$ be an equivalence relation on $C$.
Let $\struct {C, \cdot}$ be a large magma.
Then $\struct {C, \cdot}$ is a '''semigroup with respect to $\thickapprox$''' {{iff}}:
:$\forall x, y,z \in C: \paren {x \cdot y} \cdot z \thickapprox x \cdot \paren {y \cdot z}$
\end{definition}