There are accounts according to which St. Hippolytus and St. Pontian were reconciled with each other, some say before the persecution, some say in the mines. But all of these accounts are quite late, and could very well be hypotheses about why St. Hippolytus of Rome, Martyr and antipope, is celebrated on the same day as his opponent, St. Pontian, Pope and Martyr. We don't really know at all. But, one way or another, the brotherhood of martyrdom is itself a great reconciler.
From a fragment of what seems to be St. Hippolytus work, The Refutation of All Heresies:
The Logos alone of this God is from God himself; wherefore also the Logos is God, being the substance of God. Now the world was made from nothing; wherefore it is not God; as also because this world admits of dissolution whenever the Creator so wishes it. But God, who created it, did not, nor does not, make evil. He makes what is glorious and excellent; for He who makes it is good. Now man, that was brought into existence, was a creature endued with a capacity of self-determination, yet not possessing a sovereign intellect, nor holding sway over all things by reflection, and authority, and power, but a slave to his passions, and comprising all sorts of contrarieties in himself. But man, from the fact of his possessing a capacity of self-determination, brings forth what is evil, that is, accidentally; which evil is not consummated except you actually commit some piece of wickedness. For it is in regard of our desiring anything that is wicked, or our meditating upon it, that what is evil is so denominated. Evil had no existence from the beginning, but came into being subsequently. Since man has free will, a law has been defined for his guidance by the Deity, not without answering a good purpose. For if man did not possess the power to will and not to will, why should a law be established? For a law will not be laid down for an animal devoid of reason, but a bridle and a whip; whereas to man has been given a precept and penalty to perform, or for not carrying into execution what has been enjoined.