# Category:Order Embeddings

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

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

An order embedding is a mapping $\phi: S \to T$ such that:

$\forall x, y \in S: x \preceq_1 y \iff \phi \left({x}\right) \preceq_2 \phi \left({y}\right)$

## Subcategories

This category has only the following subcategory.