I pray not only for them, but also for those who will believe in me through their word, so that they may all be one, as you, Father, are in me and I in you, that they also may be in us, that the world may believe that you sent me. And I have given them the glory you gave me, so that they may be one, as we are one, I in them and you in me, that they may be brought to perfection as one, that the world may know that you sent me, and that you loved them even as you loved me.—St. John 17:20-23
The Pope, Bishop of Rome and Peter’s successor, is the perpetual and visible source and foundation of the unity both of the bishops and of the whole company of the faithful. For the Roman Pontiff, by reason of his office as Vicar of Christ, and as pastor of the entire Church has full, supreme, and universal power over the whole Church, a power which he can always exercise unhindered.
The college or body of bishops has no authority unless united with the Roman Pontiff, Peter’s successor, as its head. As such, this college has supreme and full authority over the universal Church; but this power cannot be exercised without the agreement of the Roman Pontiff.
The Greek roots of the term "Catholic" mean "according to (kata) the whole (holos)," or more colloquially, "universal." At the beginning of the second century, we find in the letters of Ignatius the first surviving use of the term "Catholic" in reference to the Church. At that time, or shortly thereafter, it was used to refer to a single, visible communion, separate from others.—Catholic Answers.
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"We must hold to the Christian religion and to communication in her Church, which is catholic and which is called catholic not only by her own members but even by all her enemies. For when heretics or the adherents of schisms talk about her, not among themselves but with strangers, willy-nilly they call her nothing else but Catholic. For they will not be understood unless they distinguish her by this name which the whole world employs in her regard" (The True Religion 7:12 [A.D. 390]).
"We believe in the holy Church, that is, the Catholic Church; for heretics and schismatics call their own congregations churches. But heretics violate the faith itself by a false opinion about God; schismatics, however, withdraw from fraternal love by hostile separations, although they believe the same things we do. Consequently, neither heretics nor schismatics belong to the Catholic Church; not heretics, because the Church loves God, and not schismatics, because the Church loves neighbor" (Faith and Creed 10:21 [A.D. 393]).—St. Augustine.
*** UPDATE!—h/t NLM: Pope creates new sui juris church!