Definition:Semigroup with respect to Equivalence Relation

Definition
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 $\thickapprox$ :
 * $\forall x, y,z \in C: \paren {x \cdot y} \cdot z \thickapprox x \cdot \paren {y \cdot z}$

Stronger properties

 * Definition:Semigroup
 * Definition:Commutative Semigroup with respect to Equivalence Relation
 * Definition:Commutative Semigroup