# Category:Restrictions

This category contains results about Restrictions.
Definitions specific to this category can be found in Definitions/Restrictions.

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

Let $X \subseteq S$, $Y \subseteq T$.

The restriction of $\mathcal R$ to $X \times Y$ is the relation on $X \times Y$ defined as:

$\mathcal R {\restriction_{X \times Y} }: = \mathcal R \cap \paren {X \times Y}$

If $Y = T$, then we simply call this the restriction of $\mathcal R$ to $X$, and denote it as $\mathcal R {\restriction_X}$.

## Subcategories

This category has the following 3 subcategories, out of 3 total.