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What the Catechism of the Catholic Church says on the "Papacy:"

869. "The Church is apostolic. She is built on a lasting foundation: 'the twelve apostles of the Lamb' [Rev 21:14.]. She is indestructible (cf. Mt 16:18). She is upheld infallibly in the truth: Christ governs her through Peter and the other apostles, who are present in their successors, the Pope and the college of bishops."

881. "The Lord made Simon alone, whom he named Peter, the 'rock' of his Church. He gave him the keys of his Church and instituted him shepherd of the whole flock. [Cf. Mt 16:18-19; Jn 21:15-17 .] 'The office of binding and loosing which was given to Peter was also assigned to the college of apostles united to its head.' [LG 22 # 2.] This pastoral office of Peter and the other apostles belongs to the Church's very foundation and is continued by the bishops under the primacy of the Pope."

882. "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.' [LG 23.] '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.' [LG 22; cf. CD 2,9.]"

895. "'The power which they exercise personally in the name of Christ, is proper, ordinary, and immediate, although its exercise is ultimately controlled by the supreme authority of the Church.' [LG 27.] But the bishops should not be thought of as vicars of the Pope. His ordinary and immediate authority over the whole Church does not annul, but on the contrary confirms and defends that of the bishops. Their authority must be exercised in communion with the whole Church under the guidance of the Pope."

Peter & Succession (Understanding the Church Today)

Pope: may all Christians recognize true meaning of Peter’s primacy

THE PRIMACY OF THE SUCCESSOR OF PETER IN THE MYSTERY OF THE CHURCH

Pope St. Leo the Great and the Petrine Primacy

THE PRIMACY OF THE SUCCESSOR OF PETER IN THE MYSTERY OF THE CHURCH [Ratzinger]

2051 The infallibility of the Magisterium of the Pastors extends to all the elements of doctrine, including moral doctrine, without which the saving truths of the faith cannot be preserved, expounded, or observed.

891 "The Roman Pontiff, head of the college of bishops, enjoys this infallibility in virtue of his office, when, as supreme pastor and teacher of all the faithful - who confirms his brethren in the faith he proclaims by a definitive act a doctrine pertaining to faith or morals. . . . The infallibility promised to the Church is also present in the body of bishops when, together with Peter's successor, they exercise the supreme Magisterium," above all in an Ecumenical Council. When the Church through its supreme Magisterium proposes a doctrine "for belief as being divinely revealed," and as the teaching of Christ, the definitions "must be adhered to with the obedience of faith." This infallibility extends as far as the deposit of divine Revelation itself.

2035 The supreme degree of participation in the authority of Christ is ensured by the charism of infallibility. This infallibility extends as far as does the deposit of divine Revelation; it also extends to all those elements of doctrine, including morals, without which the saving truths of the faith cannot be preserved, explained, or observed.

889 In order to preserve the Church in the purity of the faith handed on by the apostles, Christ who is the Truth willed to confer on her a share in his own infallibility. By a "supernatural sense of faith" the People of God, under the guidance of the Church's living Magisterium, "unfailingly adheres to this faith."

890 The mission of the Magisterium is linked to the definitive nature of the covenant established by God with his people in Christ. It is this Magisterium's task to preserve God's people from deviations and defections and to guarantee them the objective possibility of professing the true faith without error. Thus, the pastoral duty of the Magisterium is aimed at seeing to it that the People of God abides in the truth that liberates. To fulfill this service, Christ endowed the Church's shepherds with the charism of infallibility in matters of faith and morals. The exercise of this charism takes several forms: