Which means, of course, that the Cathars and Albigensians were not heretics, but a separate religion.
But to admit that would be to admit that these people were exterminated by the Church simply for belonging to a different religion. So while stating the definitions that deny its claim of heresy against them, the Church simultaneously continues to classify them as heretics anyway, in order to justify their slaughter.
Nothing to see here, move along.
What slaughter?
The crusader army came under the command, both spiritually and militarily, of the papal legate Arnaud-Amaury, Abbot of Cîteaux. In the first significant engagement of the war, the town of Béziers was besieged on 22 July 1209. The Catholic inhabitants of the city were granted the freedom to leave unharmed, but many refused and opted to stay and fight alongside the Cathars.
The Cathars spent much of 1209 fending off the crusaders. The leader of the crusaders, Simon de Montfort, resorted to primitive psychological warfare. He ordered his troops to gouge out the eyes of 100 prisoners, cut off their noses and lips, then send them back to the towers led by a prisoner with one remaining eye. This only served to harden the resolve of the Cathars.
From May 1243 to March 1244, the Cathar fortress of Montségur was besieged by the troops of the seneschal of Carcassonne and the archbishop of Narbonne. On 16 March 1244, a large and symbolically important massacre took place, where over 200 Cathar Perfects were burnt in an enormous fire at the prat dels cremats near the foot of the castle. Moreover, the Church decreed lesser chastisements against laymen suspected of sympathy with Cathars, at the 1235 Council of Narbonne.
Repentant lay believers were punished, but their lives were spared as long as they did not relapse. Having recanted, they were obliged to sew yellow crosses onto their outdoor clothing and to live apart from other Catholics, at least for a while. http://en.wikipedia.org/wiki/Cathar
As for other dissidents,
Canons of the Ecumenical Fourth Lateran Council (canon 3), 1215:
We excommunicate and anathematize every heresy that raises against the holy, orthodox and Catholic faith which we have above explained; condemning all heretics under whatever names they may be known, for while they have different faces they are nevertheless bound to each other by their tails, since in all of them vanity is a common element.
Those condemned, being handed over to the secular rulers of their bailiffs, let them be abandoned, to be punished with due justice, clerics being first degraded from their orders. As to the property of the condemned, if they are laymen, let it be confiscated; if clerics, let it be applied to the churches from which they received revenues.
But those who are only suspected, due consideration being given to the nature of the suspicion and the character of the person, unless they prove their innocence by a proper defense, let them be anathematized and avoided by all until they have made suitable satisfaction; but if they have been under excommunication for one year, then let them be condemned as heretics.
Secular authorities, whatever office they may hold, shall be admonished and induced and if necessary compelled by ecclesiastical censure, that as they wish to be esteemed and numbered among the faithful, so for the defense of the faith they ought publicly to take an oath that they will strive in good faith and to the best of their ability to exterminate in the territories subject to their jurisdiction all heretics pointed out by the Church; so that whenever anyone shall have assumed authority, whether spiritual or temporal, let him be bound to confirm this decree by oath.
But if a temporal ruler, after having been requested and admonished by the Church, should neglect to cleanse his territory of this heretical foulness, let him be excommunicated by the metropolitan and the other bishops of the province. If he refuses to make satisfaction within a year, let the matter be made known to the supreme pontiff, that he may declare the rulers vassals absolved from their allegiance and may offer the territory to be ruled lay Catholics, who on the extermination of the heretics may possess it without hindrance and preserve it in the purity of faith;
The same law is to be observed in regard to those who have no chief rulers (that is, are independent). Catholics who have girded themselves with the cross for the extermination of the heretics, shall enjoy the indulgences and privileges granted to those who go in defense of the Holy Land.(http://www.fordham.edu/halsall/basis/lateran4.asp)
This indulgence has now been transferred to those who spam FR with RC propaganda, or posts to themselves.