 The range of a history preserving function is always a prefix closed subset, where a subset "S ⊆ P" is prefix closed if for all "s,t ∈ P" with "t∈S" and "s≤t" we find "s∈S".Taking history preserving maps as "morphisms" in the category 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" of the original prefix orders.