Documents: Popes on the Cathars

Leo XIII claims that the Cathars were defeated not by human force, but by Mary's Rosary:

8. Moreover, we may well believe that the Queen of Heaven herself has granted an especial efficacy to this mode of supplication, for it was by her command and counsel that the devotion was begun and spread abroad by the holy Patriarch Dominic as a most potent weapon against the enemies of the faith at an epoch not, indeed, unlike our own, of great danger to our holy religion. The heresy of the Albigenses had in effect, one while covertly, another while openly, overrun many countries, and this most vile offspring of the Manicheans, whose deadly errors it reproduced, were the cause in stirring up against the Church the most bitter animosity and a virulent persecution. There seemed to be no human hope of opposing this fanatical and most pernicious sect when timely succour came from on high through the instrument of Mary's Rosary. Thus under the favour of the powerful Virgin, the glorious vanquisher of all heresies, the forces of the wicked were destroyed and dispersed, and faith issued forth unharmed and more shining than before.

Pius XI elaborates on The Rosary  and likens Catharism to Communism

19. The Holy Virgin who once victoriously drove the terrible sect of the Albigenses from Christian countries, now suppliantly invoked by us, will turn aside the new errors, especially those of Communism, which reminds us in many ways, in its motives and misdeeds, of the ancient ones.

20. And as in the times of the Crusades, in all Europe there was raised one voice of the people, one supplication; so today, in all the world, the cities, and even the smallest villages, united with courage and strength, with filial and constant insistence, the people seek to obtain from the great Mother of God the defeat of the enemies of Christian and human civilization, to the end that true peace may shine again over tired and erring men.