31 In reply the Roman Pontiff writes that 'he had embraced Cyril as though present in his letter,' since it was clear that 'they were of one mind concerning the Lord.' So orthodox was the faith of this Doctor that the Sovereign Pontiff delegated to him the authority of the Apostolic See, in virtue of which he was to give effect to the decrees which had already been issued against Nestorius in the Synod of Rome. And it is evident, Venerable Brethren, that at the Council of Ephesus the Patriarch of Alexandria acted as the legal representative of the Roman Pontiff; for, although the latter also sent his own Legates, the chief instruction he gave them was that they should support the action and the authority of St. Cyril. It was therefore in the name of the Sovereign Pontiff that he presided at this holy Council, and he w as the first to sign its proceedings. Indeed, so manifest was the agreement between the Apostolic See and that of Alexandria that, after the public reading of St. Celestine's letter in the second session of the Council, the Fathers exclaimed: This judgment is just. To Celestine, a new Paul; to Cyril, a new Paul; to Celestine, guardian of the faith; to Celestine, who is of one mind with the Synod, the whole of this Synod gives thanks. One Celestine, one Cyril, one faith of the Synod, one faith of the whole world.
Source: Orientalis Ecclesiae (Vatican.va)