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<p>of a history preserving function is always a <a href="page.php?w=prefix_closed">prefix closed</a> subset, where a subset S ? P is <b>prefix closed</b> if for all s,t ? P with t?S and s<=t</i> we find s?S.</=t</i></p>

<p><big> Product and union </big></p>
<p>Taking history preserving maps as morphisms in the <a href="page.php?w=category_theory">category</a> of prefix orders leads to a notion of product that is not the Cartesian product of the two orders since the Cartesian product is not always a prefix order. Instead, it leads to an arbitrary interleaving</p><p>
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