= Solution
A <poset> becomes a <category> whose objects are its elements and whose <hom-set> $X(x,y)$ is a singleton if $x\le y$ and empty otherwise. Reflexivity supplies identity arrows and transitivity supplies composition; all possible composites are unique, so the <category> axioms hold. Antisymmetry says that isomorphic objects are equal. A <functor> between such <categories> is exactly an <order-preserving function>: an inequality must be sent to an inequality, and there is no further choice of arrow map.
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