# Category:Definitions/Compatible Relations

This category contains definitions related to Compatible Relations.
Related results can be found in Category:Compatible Relations.

Let $\struct {S, \circ}$ be a closed algebraic structure.

Let $\mathcal R$ be a relation on $S$.

Then $\mathcal R$ is compatible with $\circ$ if and only if:

$\forall x, y, z \in S: x \mathrel {\mathcal R} y \implies \paren {x \circ z} \mathrel {\mathcal R} \paren {y \circ z}$
$\forall x, y, z \in S: x \mathrel {\mathcal R} y \implies \paren {z \circ x} \mathrel {\mathcal R} \paren {z \circ y}$

## Subcategories

This category has only the following subcategory.

## Pages in category "Definitions/Compatible Relations"

The following 3 pages are in this category, out of 3 total.