Relating to an archbishop or the office and authority of an archbishop.
From Medieval Latin 'archiepiscopalis,' combining 'archi-' (chief) with 'episcopalis' (relating to a bishop), formed when the church needed to distinguish senior bishops from regular ones.
The Roman Catholic Church created this whole hierarchy of 'arch-' positions to organize power—archbishop, archduke, archdeacon—and it's still the language they use because changing it would require the Pope to literally rewrite church law.
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