Universal jurisdiction, as traditionally understood, is tied up in notions of territoriality. The very question of jurisdiction in international law is territorially derived, depending mostly on where a crime was committed or where an alleged perpetrator or victim holds nationality. So when states apply universal jurisdiction, bypassing the traditional bases of jurisdiction, extra-territoriality is said to be at play.
the prescriptive reach of universal jurisdiction is not really extraterritorial; rather, it comprises a comprehensive territorial jurisdiction, originating in a universally applicable international law that covers the globe. Individual states may apply and enforce that law in domestic courts, to be sure, but its prescriptive scope encompasses all territory subject to international law, i.e., the entire world.
Note the contrasting imagery. The idea of extraterritoriality takes traditional state sovereignty as its default starting point—universal jurisdiction is treated as a departure from the norm. This hang-up with territory and physical geography may be descriptively accurate of the current international system; but as Colangelo suggests, it’s prescriptively inadequate. Universal jurisdiction begins more soundly from the premise that international crimes can be applicable anywhere. To be sure, this alternative geography requires a social conception of space: recognition that what makes some crimes international is the reprobation they evoke, not whether their effects spill over across borders as would a material pollutant.
If extraterritoriality is depicted with lines linking states to one another, universal jurisdiction would be more like an all-encompassing sphere, to some extent transcending the inter-state system. These represent two very different conceptual maps, with varying implications for how we see the world of universal jurisdiction.