A retract is a pair formula_23 of order-preserving maps whose composition formula_24 is the identity. In this case, formula_4 is called a coretraction, and must be an order embedding. However, not every order embedding is a coretraction. As a trivial example, the unique order embedding formula_26 from the empty poset to a nonempty poset has no retract, because there is no order-preserving map formula_27. More illustratively, consider the set formula_7 of divisors of 6, partially ordered by "x" divides "y", see picture. Consider the embedded sub-poset formula_29. A retract of the embedding formula_30 would need to send formula_31 to somewhere in formula_29 above both formula_33 and formula_34, but there is no such place.