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A separoid is a symmetric relation $†\subset \left(\genfrac{}{}{0pt}{}{2^S}{2}\right)$ defined on disjoint pairs of subsets of a given set $S$ such that it is closed as a filter in the canonical partial order induced by the inclusion (i.e., $A†B⪯A^{\text{'}}†B^{\text{'}}\iff A\subseteq A^{\text{'}}$ and $B\subseteq B^{\text{'}}$). We introduce the notion of homomorphism as a map which preserve the so-called “minimal Radon partitions” and show that separoids, endowed with these maps, admits an embedding from the category of all finite graphs. This proves that separoids constitute a countable universal partial order. Furthermore,...