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In [[computer science]], algorithms for finding linear extensions of partial orders (represented as the [[reachability]] orders of [[directed acyclic graph]]s) are called [[topological sorting]].
== In [[category theory]] ==
{{main|Posetal category}}
Every poset (and every [[Preorder|preordered set]]) may be considered as a [[Category (mathematics)|category]] where, for objects <math>x</math> and <math>y,</math> there is at most one [[morphism]] from <math>x</math> to <math>y.</math> More explicitly, let {{nowrap|1=hom(''x'', ''y'') = {{mset|(''x'', ''y'')}}}} if {{nowrap|''x'' ≤ ''y''}} (and otherwise the [[empty set]]) and <math>(y, z) \circ (x, y) = (x, z).</math> Such categories are sometimes called ''[[Posetal category|posetal]]''.
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