From Rev. Fr. Paul Bottala, S.J. of happy memory, The Pope and the Church Considered in their Mutual Relations, Part 2 – The Infallibility of the Pope, pp. 243-246:
We say, then, that the Fifth Synod professed adherence in principle as well as in fact to the judgments of the Apostolic See, although its Decree did not properly regard doctrines of faith. … When Justinian forced the Patriarchs and Bishops of the East to sign his edict of condemnation against the Three Chapters, Mennas, patriarch of Constantinople [536-552], openly declared that he could not sign it without the consent of the Apostolic See,602 and when forced to subscribe, he submitted on the condition that his act of adhesion should be returned to him in case the Pope refused to ratify it.603 Zoilus, Patriarch of Alexandria [541-551], went to meet Pope Vigilius in Sicily in order to justify his conduct in yielding to violence and signing the imperial edict.604 Facundus Hermianensis testifies the same of the other Oriental Bishops who had been compelled to put their signature to the edict of the Prince [Ephraim of Antioch (526-546) and Peter of Jerusalem (524-552)].605 When the Synod met in Constantinople, the Fathers were most anxious that the Pope should pronounce his judgment on the subject of the Three Chapters; and Vigilius referred to the right of his See to be the first to give sentence.606
602 Facundus Herm., De Tribus Capitulis, l. iv, cap. iv (Gallandi, t. xi, p. 708).
603 Ibid., l. c.
604 Ibid., l. c.
605 Ibid., l. c.
606 In Constituto (Labbe, t. v., p. 1320).
Pope Vigilius, therefore, after a lapse of six months from the end of the Synod, addressed a Letter to the Patriarch Eutychius, in which he condemned the works and the name of Theodorus, as well as those writings of Theodoret and Ibas which favored Nestorius.610 But in this document, as well as in the new Constitutum, which was perhaps addressed to the Eastern Bishops,611 he made no mention whatever of the Fifth Council; and the purpose of this omission was to show that other considerations, and not the authority of a Synod which was yet unrecognized, had brought him to this new resolution. Then, and only then, the Synod of Constantinople began to have authority in the Church, and to be ranked among the Ecumenical Councils.
610 Epist. Decretalis Vigilii Papae ad Eutychium (Labbe, t. vi, p. 239, seq. In Migne, t. lxix, PP. LL., p. 121, seq.).
611 Constitutum Vigilii Papae pro damnatione Trium Capitulorum (Labbe, t. vi, p. 281, seq. In Migne, l. c., p. 143, seq.).