# Category:Order Isomorphisms

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

Let $\left({S, \preceq_1}\right)$ and $\left({T, \preceq_2}\right)$ be ordered sets.

Let $\phi: S \to T$ be a bijection such that:

$\phi: S \to T$ is order-preserving
$\phi^{-1}: T \to S$ is order-preserving.

Then $\phi$ is an order isomorphism.

## Subcategories

This category has the following 2 subcategories, out of 2 total.