Allow me to explain this a little more in detail. The Roman Catholic Church teaches that supreme authority can be exercised in the Church either personally by the pope, or collegially by the whole episcopate which includes the pope as its head so that there are not two separate supreme authorities that could ever come into conflict.
The pope, as head of the body, remains free to decide whether a particular decision calls for collegial action or not. The other bishops, even collectively, have no authority to oblige the pope to choose the collegial rather than the personal exercise of supreme power in any given case. The fact that they can share in acts of universal jurisdiction does not give them such a right to do so as that would conflict with the pope’s liberty to exercise his supreme authority as he judges best [Nota explicativa 3–4; Acta Apostolicae Sedis 57 (1965) 74–75] as per the doctrine of papal primacy with the plenitude of authority the Vatican Council I defined the pope to have.
This is why ex cathedra (canonized in the language of the Church in the definition of papal infallibility as per Enchiridion symbolorum, 3074) symbolically expresses the supreme authority within the Church of the Roman pontiff. Extended in the form of ex cathedra Petri, it symbolizes the Roman pontiff’s title to that supreme authority and to the infallibility that accompanies it as successor of Peter head of the college of the Apostles. The RCC teaches that through succession to his chair, or supreme office in the Church, the authority and infallibility of Peter lives on in the Roman pontiff.
All of that said, the answer is yes: more like option 2.