For a short while, including Augustine’s time, there were a group of schismatics called “Luciferians,” followers of Lucifer of Cagliari, so fierce an opponent of the Arians that he zealously opposed any attempt to reconcile Arians to the Church. What Augustine detested in the Luciferians was that they were willing to be cut off from their Catholic root.

What they did not like about the Catholic Church was that it displayed a Catholic holiness. For nowhere should the “bowels of mercy” (see Col 3:12) flourish as much as in the Catholic Church who, like a true mother, neither proudly assails her sinful children nor finds it difficult to forgive them when they have been corrected. There is good reason why, among all the Apostles, Peter personifies this Catholic Church, for it was to that Church that the keys of the Kingdom of heaven were given when they were given to Peter (Mt 16:19). And what is said to him is said to all, “Do you love me? Feed my sheep” (Jn 21:17). The Catholic Church, then, should willingly forgive her children when they have been corrected and strengthened in their piety, for it was to Peter who personified her when he tottered on the sea (Mt 14:30), and when, thinking according to the flesh, he called the Lord back from his passion (Mt 16:22), and when he cut off the servant’s ear (Mt 26:51), and when he denied the Lord himself three times (Mt 26: 70-74), and when later he lapsed into superstitious simulation (Gal 2:12)–it was to this Church-personifying Peter that we see pardon was granted, and he, when corrected and strengthened, reached the glory of the Lord’s passion.  (Augustine, On Christian combat, XXX, 32; PL 40, 308)