Saint Cornelius was elected Pope in 251 during the persecutions of the Emperor Decius. His first challenge, besides the ever present threat of the Roman authorities, was to bring an end to the schism brought on by his rival, the first anti-pope Novatian. He convened a synod of bishops to confirm him as the rightful successor of Peter.

The great controversy that arose as a result of the Decian persecution was whether or not the Church could pardon and receive back into the Church those who had apostacized in the face of martyrdom.

Against both the bishops who argued that the Church could not welcome back apostates, and those who argued that they should be welcomed back but did not demand a heavy penance of the penitent, Cornelius decreed that they must be welcomed back and insisted that they perform an adequate penance.

In 253 Cornelius was exiled by the emperor Gallus and died of the hardships he endured in exile. He is venerated as a martyr.

Saint Cyprian of Carthage is second in importance only to the great Saint Augustine as a figure and Father of the African church. He was a close friend of Pope Cornelius, and supported him both against the anti-pope Novatian and in his views concerning the re-admittance of apostates into the Church.

Saint Cyprian was born to wealthy pagans around the year 190, and was educated in the classics and in rhetoric. He converted at the age of 56, was ordained a priest a year later, and made bishop two years after that.

Source:

http://www.catholicnewsagency.com/saint.php?n=596