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Ad abolendam ("On abolition" or "Towards abolishing") was a decretal and bull of Pope Lucius III, written at Verona in November 1184. It was developed after the Council of Verona settled some jurisdictional differences between the Papacy and the Holy Roman Emperor Frederick Barbarossa. The document prescribes measures to uproot heresy and sparked the efforts which culminated in the Albigensian Crusade and the Inquisitions. Its chief aim was the complete abolition of Christian heresy.
Lucius condemned all heretical sects and persons who preached without the authorisation of the Roman Church, whether publicly or privately, and placed them under excommunication. Among the particular sects mentioned in Ad abolendam were the Cathars, Humiliati, Waldensians, Arnoldists, and Josephines. More important than the direct attack on heresy, however, was the stipulation of equal measures for those who supported heretics, overtly or indirectly. They too were placed under excommunication.
Those accused of heresy, if they could not prove their innocence or forswear their errors, or if they backslid into error subsequently, were to be handed over to the lay authorities to receive their animadversio debita ("due penalty"). All those who supported heresy were deprived of their many rights: the right to hold public office, the right to trial, the right to draft a will, and the hereditability of their fiefs and offices.
For the enforcement of the measures demanded by the decretal, Lucius obligated all patriarchs, archbishops, and bishops to re-announce the excommunication on certain feasts and holidays. Those who did not observe this for three years consecutively would be deprived of their ecclesiastical offices. The bishops were furthermore obligated to "seek out" heretics. They were to make bi- or triannual rounds of their dioceses, visiting locations of suspicion and question the people about the existence of heresy. The people would be required to swear under oath (compurgation) anything they knew about heretical activity. All oath-breakers were to be treated as heretics.
The bull was incorporated as Canon 3 of the Fourth Council of the Lateran of 1215 under Pope Innocent III. Contrary to what is often said, Lucius did not institute the Inquisition, which was not created until the reign of Pope Gregory IX in 1234.