True. There was no concept of separation of Church and “state” (even the latter concept did not yet exist in the modern sense) during the Middle Ages - and in many places well into the early modern period. It was understood, in theory, in the West, that the pope exercised the plenitude of spiritual authority and the emperor the plenitude of temporal power - but the lines were often blurred. In both East and West kings/emperors were anointed by the Church to carry out the sacred function of government, so it wouldn’t have seemed so odd for temporal rulers to appoint bishops
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